{"id":690,"date":"2026-07-31T23:54:13","date_gmt":"2026-07-31T23:54:13","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=690"},"modified":"2026-07-31T23:54:15","modified_gmt":"2026-07-31T23:54:15","slug":"physics-constants","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/physics-constants\/","title":{"rendered":"Physics Constants: Values, Units and Where to Use Them"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nPhysics constants are fixed quantities that appear in physical laws and take the same value everywhere in the universe. Seven of them now define the SI exactly, including the speed of light c = 299,792,458 m\/s and the Planck constant h = 6.62607015 \u00d7 10<sup>-34<\/sup> J s. Others, such as the gravitational constant G, must still be measured.\n<\/p><\/div>\n\n<p>On 20 May 2019, a polished cylinder of platinum-iridium sitting in a vault outside Paris quietly stopped being the kilogram. It had defined mass for 130 years. Its replacement is a number: the Planck constant, fixed forever at 6.62607015 \u00d7 10<sup>-34<\/sup> J s.<\/p>\n\n<p>That swap tells you what these numbers really are. A constant is not trivia to memorise before an exam \u2014 it is the anchor that ties an equation to the physical world, and increasingly it <em>is<\/em> the definition of the unit itself.<\/p>\n\n<h2>What Are Physics Constants?<\/h2>\n\n<p>Physics constants are quantities whose value does not change with time, place, or the experiment being run, and which appear in the equations describing how nature behaves. Some are fixed by definition; others are measured, and carry an uncertainty.<\/p>\n\n<p>That distinction matters more than most textbooks admit. Lump them together and you end up quoting <em>g<\/em> to nine decimal places, or treating G as though it were known as precisely as c. Neither is true.<\/p>\n\n<p>It helps to sort them into four honest categories:<\/p>\n\n<ul>\n<li><strong>Defining constants.<\/strong> Exact by international agreement, with zero uncertainty. c, h, e, k and N<sub>A<\/sub> are in this group.<\/li>\n<li><strong>Derived exact constants.<\/strong> Built from defining constants by pure arithmetic, so also exact \u2014 though irrational. R and the Stefan-Boltzmann constant \u03c3 sit here.<\/li>\n<li><strong>Measured constants.<\/strong> Known only as well as the best experiment allows. G is the classic case.<\/li>\n<li><strong>Conventional or conditional values.<\/strong> Agreed for convenience, or true only under stated conditions. Standard gravity <em>g<\/em> and the speed of sound in air both belong here.<\/li>\n<\/ul>\n\n<p>Only the first two are genuinely universal in the strict sense. The last group is the one students trip over, and we will come back to it.<\/p>\n\n<h2>Physics Constants Reference Table<\/h2>\n\n<p>The table below lists the constants you will meet in school and first-year university physics, with the CODATA 2022 values <a href=\"https:\/\/physics.nist.gov\/cuu\/Constants\/\" target=\"_blank\" rel=\"noopener\">published by NIST<\/a>, SI units, and whether each one is exact or measured.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Constant<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Symbol<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Value<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">SI unit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Status<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Standard gravity<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>g<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">9.80665 (use 9.81)<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">m\/s\u00b2<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Conventional<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Speed of light in vacuum<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>c<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">299,792,458<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">m\/s<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Planck constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>h<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">6.62607015 \u00d7 10<sup>-34<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">J s<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Reduced Planck constant (h-bar)<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>h<\/em>\/2\u03c0<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">1.054571817&#8230; \u00d7 10<sup>-34<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">J s<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact (derived)<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Gravitational constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>G<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">6.67430(15) \u00d7 10<sup>-11<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">m\u00b3 kg<sup>-1<\/sup> s<sup>-2<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Measured (22 ppm)<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Molar gas constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>R<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">8.314462618&#8230;<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">J mol<sup>-1<\/sup> K<sup>-1<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact (derived)<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Boltzmann constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>k<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">1.380649 \u00d7 10<sup>-23<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">J\/K<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Avogadro constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>N<\/em><sub>A<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">6.02214076 \u00d7 10<sup>23<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">mol<sup>-1<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Elementary charge<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>e<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">1.602176634 \u00d7 10<sup>-19<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">C<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Coulomb constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>k<\/em><sub>e<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">8.98755179 \u00d7 10<sup>9<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">N m\u00b2 C<sup>-2<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Derived<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Vacuum permittivity<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">\u03b5<sub>0<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">8.8541878188(14) \u00d7 10<sup>-12<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">F\/m<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Measured<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Vacuum permeability<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">\u03bc<sub>0<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">1.25663706127(20) \u00d7 10<sup>-6<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">N\/A\u00b2<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Measured<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Stefan-Boltzmann constant<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">\u03c3<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">5.670374419&#8230; \u00d7 10<sup>-8<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">W m<sup>-2<\/sup> K<sup>-4<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact (derived)<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Electron mass<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>m<\/em><sub>e<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">9.1093837139(28) \u00d7 10<sup>-31<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">kg<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Measured<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Proton mass<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>m<\/em><sub>p<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">1.67262192595(52) \u00d7 10<sup>-27<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">kg<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Measured<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">Speed of sound in air (20 \u00b0C)<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>v<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">343<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">m\/s<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Conditional<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Trailing dots mean the decimal expansion never terminates, but the value is still exact. Digits in brackets are the standard uncertainty in the final two figures, so 6.67430(15) means 6.67430 \u00b1 0.00015.<\/p>\n\n<p>If you need constants beyond this working set, NIST publishes the full CODATA list as a <a href=\"https:\/\/physics.nist.gov\/cuu\/pdf\/wall_2022.pdf\" target=\"_blank\" rel=\"noopener\">one-page wall chart<\/a>.<\/p>\n\n<h2>Why the SI Is Now Built on Seven Defining Constants<\/h2>\n\n<p>Since 20 May 2019, every SI base unit has been defined by fixing the numerical value of a constant of nature rather than by a physical artefact, as set out in the <a href=\"https:\/\/www.bipm.org\/en\/measurement-units\" target=\"_blank\" rel=\"noopener\">BIPM definition of the SI<\/a>. The kilogram now follows from the Planck constant; the metre follows from the speed of light.<\/p>\n\n<p>Think of it as changing the reference from a ruler in a drawer to a property of the universe. Anyone with the right apparatus can rebuild the kilogram in Nairobi or Nagoya and get the same answer, because the definition travels as a number rather than a lump of metal.<\/p>\n\n<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 700 482\" role=\"img\" aria-label=\"The seven SI defining constants and the seven base units each one fixes\" style=\"width:100%;height:auto;\">\n<rect x=\"0\" y=\"0\" width=\"700\" height=\"482\" rx=\"6\" fill=\"#0A1628\"><\/rect>\n<text x=\"24\" y=\"34\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#FAF6EE\">The seven SI defining constants<\/text>\n<text x=\"24\" y=\"54\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"12\" fill=\"#C5D0DC\">Each fixed number on the left defines the unit on the right \u2014 exactly, with zero uncertainty.<\/text>\n<rect x=\"24\" y=\"76\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"102\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">\u0394\u03bd<tspan font-size=\"11\" dy=\"3\">Cs<\/tspan><\/text>\n<text x=\"86\" y=\"102\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 9 192 631 770 Hz<\/text>\n<line x1=\"376\" y1=\"97\" x2=\"470\" y2=\"97\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,97 462,93 462,101\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"76\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"102\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">second<\/text>\n<text x=\"652\" y=\"102\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">s<\/text>\n<rect x=\"24\" y=\"130\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"156\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">c<\/text>\n<text x=\"86\" y=\"156\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 299 792 458 m\/s<\/text>\n<line x1=\"376\" y1=\"151\" x2=\"470\" y2=\"151\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,151 462,147 462,155\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"130\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"156\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">metre<\/text>\n<text x=\"652\" y=\"156\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">m<\/text>\n<rect x=\"24\" y=\"184\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"210\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">h<\/text>\n<text x=\"86\" y=\"210\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 6.626 070 15 \u00d7 10<tspan font-size=\"11\" dy=\"-7\">-34<\/tspan><tspan dy=\"7\"> J s<\/tspan><\/text>\n<line x1=\"376\" y1=\"205\" x2=\"470\" y2=\"205\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,205 462,201 462,209\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"184\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"210\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">kilogram<\/text>\n<text x=\"652\" y=\"210\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">kg<\/text>\n<rect x=\"24\" y=\"238\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"264\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">e<\/text>\n<text x=\"86\" y=\"264\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 1.602 176 634 \u00d7 10<tspan font-size=\"11\" dy=\"-7\">-19<\/tspan><tspan dy=\"7\"> C<\/tspan><\/text>\n<line x1=\"376\" y1=\"259\" x2=\"470\" y2=\"259\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,259 462,255 462,263\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"238\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"264\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">ampere<\/text>\n<text x=\"652\" y=\"264\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">A<\/text>\n<rect x=\"24\" y=\"292\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"318\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">k<\/text>\n<text x=\"86\" y=\"318\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 1.380 649 \u00d7 10<tspan font-size=\"11\" dy=\"-7\">-23<\/tspan><tspan dy=\"7\"> J\/K<\/tspan><\/text>\n<line x1=\"376\" y1=\"313\" x2=\"470\" y2=\"313\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,313 462,309 462,317\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"292\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"318\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">kelvin<\/text>\n<text x=\"652\" y=\"318\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">K<\/text>\n<rect x=\"24\" y=\"346\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"372\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">N<tspan font-size=\"11\" dy=\"3\">A<\/tspan><\/text>\n<text x=\"86\" y=\"372\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 6.022 140 76 \u00d7 10<tspan font-size=\"11\" dy=\"-7\">23<\/tspan><tspan dy=\"7\"> \/mol<\/tspan><\/text>\n<line x1=\"376\" y1=\"367\" x2=\"470\" y2=\"367\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,367 462,363 462,371\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"346\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"372\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">mole<\/text>\n<text x=\"652\" y=\"372\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">mol<\/text>\n<rect x=\"24\" y=\"400\" width=\"352\" height=\"42\" rx=\"4\" fill=\"#142139\" stroke=\"#C8932A\" stroke-width=\"1\"><\/rect>\n<text x=\"40\" y=\"426\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\">K<tspan font-size=\"11\" dy=\"3\">cd<\/tspan><\/text>\n<text x=\"86\" y=\"426\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#FAF6EE\">= 683 lm\/W<\/text>\n<line x1=\"376\" y1=\"421\" x2=\"470\" y2=\"421\" stroke=\"#D9CFB8\" stroke-width=\"1.2\" opacity=\"0.75\"><\/line>\n<polygon points=\"470,421 462,417 462,425\" fill=\"#C8932A\"><\/polygon>\n<rect x=\"476\" y=\"400\" width=\"200\" height=\"42\" rx=\"4\" fill=\"#F5F2EA\"><\/rect>\n<text x=\"492\" y=\"426\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\">candela<\/text>\n<text x=\"652\" y=\"426\" text-anchor=\"end\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">cd<\/text>\n<text x=\"24\" y=\"470\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">In force since 20 May 2019. Source: BIPM, SI Brochure (9th edition).<\/text>\n<\/svg>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">The seven defining constants of the SI and the base unit each one fixes.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/07\/International_prototype_of_the_kilogram_aka_Le_Grand_K.jpg\"\n       alt=\"Platinum-iridium prototype kilogram, replaced by the Planck constant among the physics constants\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" width=\"1217\" height=\"1512\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">A platinum-iridium prototype kilogram. Artefacts like this defined mass until the Planck constant took over in 2019.<\/figcaption>\n<\/figure>\n\n<p>Notice what this does to precision. Once a value is fixed by decree, its uncertainty is zero forever, and the uncertainty moves instead into how well we can <em>realise<\/em> the unit in a laboratory.<\/p>\n\n<h2>The Seven Constants You Actually Use<\/h2>\n\n<p>Five constants carry most of the load in school and first-year physics \u2014 g, c, h, G and R \u2014 with the Coulomb constant and the speed of sound close behind. Here is what each one does, and the trap that comes with it.<\/p>\n\n<h3>g \u2014 Standard Gravity<\/h3>\n\n<p>Standard gravity is the conventional acceleration of free fall near Earth&#8217;s surface, fixed at exactly 9.80665 m\/s\u00b2 by the 3rd General Conference on Weights and Measures in 1901.<\/p>\n\n<div class=\"pf-formula\">W = mg<\/div>\n\n<ul>\n<li><strong>W<\/strong> \u2014 weight, the gravitational force on the object, in newtons (N)<\/li>\n<li><strong>m<\/strong> \u2014 mass, in kilograms (kg)<\/li>\n<li><strong>g<\/strong> \u2014 gravitational field strength, in newtons per kilogram (N\/kg), numerically equal to the free-fall acceleration in m\/s\u00b2<\/li>\n<\/ul>\n\n<p>Here is the catch: <em>g<\/em> is not a constant of nature at all. Real local gravity runs from roughly 9.78 m\/s\u00b2 at the equator to about 9.83 m\/s\u00b2 at the poles, because Earth spins and bulges.<\/p>\n\n<p>In practice, use 9.81 m\/s\u00b2 unless a question specifies otherwise. The 9.80665 figure is a legal convention for trade and calibration, not a measurement of your particular hillside.<\/p>\n\n<h3>c \u2014 The Speed of Light in Vacuum<\/h3>\n\n<p>The speed of light in vacuum is exactly 299,792,458 m\/s, and has been since 1983, when the metre was redefined in terms of it.<\/p>\n\n<div class=\"pf-formula\">E = mc<sup>2<\/sup><\/div>\n\n<ul>\n<li><strong>E<\/strong> \u2014 energy, in joules (J)<\/li>\n<li><strong>m<\/strong> \u2014 mass, in kilograms (kg)<\/li>\n<li><strong>c<\/strong> \u2014 speed of light in vacuum, in metres per second (m\/s)<\/li>\n<\/ul>\n\n<p>That exactness is not a boast about measurement. It is a definition: we stopped measuring c and started using it to define length, so the metre is now whatever distance light covers in 1\/299,792,458 of a second.<\/p>\n\n<h3>h \u2014 The Planck Constant<\/h3>\n\n<p>The Planck constant relates a photon&#8217;s energy to its frequency, and is exactly 6.62607015 \u00d7 10<sup>-34<\/sup> J s.<\/p>\n\n<div class=\"pf-formula\">E = hf<\/div>\n\n<ul>\n<li><strong>E<\/strong> \u2014 photon energy, in joules (J)<\/li>\n<li><strong>h<\/strong> \u2014 Planck constant, in joule seconds (J s)<\/li>\n<li><strong>f<\/strong> \u2014 frequency, in hertz (Hz)<\/li>\n<\/ul>\n\n<p>Because h is tiny, quantum effects stay hidden at everyday scales \u2014 a single green photon carries only about 4 \u00d7 10<sup>-19<\/sup> J. If you are converting between wavelength, frequency and energy repeatedly, the <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/photon-energy\">photon energy calculator<\/a> handles the unit juggling for you.<\/p>\n\n<h3>G \u2014 The Gravitational Constant<\/h3>\n\n<p>The gravitational constant sets the strength of gravity between any two masses, with a CODATA 2022 value of 6.67430(15) \u00d7 10<sup>-11<\/sup> m\u00b3 kg<sup>-1<\/sup> s<sup>-2<\/sup>.<\/p>\n\n<div class=\"pf-formula\">F = Gm<sub>1<\/sub>m<sub>2<\/sub> \/ r<sup>2<\/sup><\/div>\n\n<ul>\n<li><strong>F<\/strong> \u2014 gravitational force, in newtons (N)<\/li>\n<li><strong>G<\/strong> \u2014 gravitational constant, in m\u00b3 kg<sup>-1<\/sup> s<sup>-2<\/sup> (equivalently N m\u00b2 kg<sup>-2<\/sup>)<\/li>\n<li><strong>m<sub>1<\/sub>, m<sub>2<\/sub><\/strong> \u2014 the two masses, in kilograms (kg)<\/li>\n<li><strong>r<\/strong> \u2014 separation between their centres, in metres (m)<\/li>\n<\/ul>\n\n<p>G is the embarrassment of precision physics. We know the electron&#8217;s magnetic moment to about one part in a trillion, yet G is pinned down only to 22 parts per million, because gravity is far too weak to shield from everything else.<\/p>\n\n<p>It is also the constant students most often confuse with <em>g<\/em>. They are not related by a shortcut; you can compute the gravitational force between any two objects with the <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/gravitational-force\">gravitational force calculator<\/a> and see how different the scales are.<\/p>\n\n<h3>R \u2014 The Molar Gas Constant<\/h3>\n\n<p>The molar gas constant links pressure, volume, amount of substance and temperature for an ideal gas, and equals exactly 8.314462618&#8230; J mol<sup>-1<\/sup> K<sup>-1<\/sup>.<\/p>\n\n<div class=\"pf-formula\">pV = nRT<\/div>\n\n<ul>\n<li><strong>p<\/strong> \u2014 pressure, in pascals (Pa)<\/li>\n<li><strong>V<\/strong> \u2014 volume, in cubic metres (m\u00b3)<\/li>\n<li><strong>n<\/strong> \u2014 amount of substance, in moles (mol)<\/li>\n<li><strong>R<\/strong> \u2014 molar gas constant, in J mol<sup>-1<\/sup> K<sup>-1<\/sup><\/li>\n<li><strong>T<\/strong> \u2014 absolute temperature, in kelvin (K)<\/li>\n<\/ul>\n\n<p>R is not fundamental in its own right. It is simply the Boltzmann constant scaled up to one mole, R = N<sub>A<\/sub>k, which is why it inherited exactness the moment both of those were fixed.<\/p>\n\n<p>Keep T in kelvin and p in pascals and the units take care of themselves; the <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/ideal-gas-law\">ideal gas law calculator<\/a> is useful for checking a rearrangement you are unsure about.<\/p>\n\n<h3>k<sub>e<\/sub> \u2014 The Coulomb Constant<\/h3>\n\n<p>The Coulomb constant sets the strength of the electrostatic force and equals 8.98755179 \u00d7 10<sup>9<\/sup> N m\u00b2 C<sup>-2<\/sup>, usually rounded to 8.99 \u00d7 10<sup>9<\/sup>.<\/p>\n\n<div class=\"pf-formula\">F = k<sub>e<\/sub>q<sub>1<\/sub>q<sub>2<\/sub> \/ r<sup>2<\/sup><\/div>\n\n<ul>\n<li><strong>F<\/strong> \u2014 electrostatic force, in newtons (N)<\/li>\n<li><strong>k<sub>e<\/sub><\/strong> \u2014 Coulomb constant, equal to 1\/(4\u03c0\u03b5<sub>0<\/sub>), in N m\u00b2 C<sup>-2<\/sup><\/li>\n<li><strong>q<sub>1<\/sub>, q<sub>2<\/sub><\/strong> \u2014 the two charges, in coulombs (C)<\/li>\n<li><strong>r<\/strong> \u2014 separation, in metres (m)<\/li>\n<\/ul>\n\n<p>Compare k<sub>e<\/sub> with G and the gulf between the two forces becomes obvious: one is around 10<sup>9<\/sup>, the other around 10<sup>-11<\/sup>. Electrostatics beats gravity by roughly twenty orders of magnitude for everyday particles.<\/p>\n\n<h3>v \u2014 The Speed of Sound in Air<\/h3>\n\n<p>The speed of sound in dry air is about 343 m\/s at 20 \u00b0C, and it changes with temperature rather than with pressure.<\/p>\n\n<div class=\"pf-formula\">v = 331.3 sqrt(1 + T\/273.15)<\/div>\n\n<ul>\n<li><strong>v<\/strong> \u2014 speed of sound in dry air, in metres per second (m\/s)<\/li>\n<li><strong>331.3<\/strong> \u2014 the speed at 0 \u00b0C, in m\/s<\/li>\n<li><strong>T<\/strong> \u2014 air temperature, in degrees Celsius (\u00b0C)<\/li>\n<\/ul>\n\n<p>This is the most conditional entry on the page. Quote 343 m\/s without stating the temperature and you have quoted a number, not a constant.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Physics Constants Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/physics-constants.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>Which Physics Constants Are Exact, and Which Are Measured?<\/h2>\n\n<p>Five constants are exact because the SI defines them: c, h, e, k and N<sub>A<\/sub>. Everything else is either arithmetic built from those, or a genuine measurement carrying an uncertainty.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Constant<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Relative uncertainty<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">In plain terms<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">c, h, e, k, N<sub>A<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">0<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact by definition<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">R, \u03c3, h\/2\u03c0<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">0<\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">Exact, built by arithmetic from the above<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">\u03b5<sub>0<\/sub>, \u03bc<sub>0<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">1.6 \u00d7 10<sup>-10<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">About 1 part in 6 billion<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\">m<sub>e<\/sub>, m<sub>p<\/sub><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">3.1 \u00d7 10<sup>-10<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">About 1 part in 3 billion<\/td><\/tr>\n<tr><td style=\"padding:9px;border:1px solid #D9CFB8;\"><em>G<\/em><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">2.2 \u00d7 10<sup>-5<\/sup><\/td><td style=\"padding:9px;border:1px solid #D9CFB8;\">About 1 part in 45,000<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Read the last two rows together and the oddity jumps out. We know the mass of a proton roughly a hundred thousand times more precisely than we know the strength of the force holding the solar system together.<\/p>\n\n<p>The values themselves are also wildly spread out, which is worth seeing rather than being told.<\/p>\n\n<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 700 250\" role=\"img\" aria-label=\"Logarithmic scale showing the physics constants spanning about 43 orders of magnitude\" style=\"width:100%;height:auto;\">\n<rect x=\"0\" y=\"0\" width=\"700\" height=\"250\" rx=\"6\" fill=\"#0A1628\"><\/rect>\n<text x=\"24\" y=\"32\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#FAF6EE\">Physics constants span 43 orders of magnitude<\/text>\n<text x=\"24\" y=\"52\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"12\" fill=\"#C5D0DC\">Numerical value in SI units, on a logarithmic scale.<\/text>\n<line x1=\"54\" y1=\"170\" x2=\"662\" y2=\"170\" stroke=\"#D9CFB8\" stroke-width=\"1.4\"><\/line>\n<line x1=\"54.0\" y1=\"165\" x2=\"54.0\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"54.0\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">-35<\/tspan><\/text>\n<line x1=\"155.3\" y1=\"165\" x2=\"155.3\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"155.3\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">-25<\/tspan><\/text>\n<line x1=\"256.7\" y1=\"165\" x2=\"256.7\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"256.7\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">-15<\/tspan><\/text>\n<line x1=\"358.0\" y1=\"165\" x2=\"358.0\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"358.0\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">-5<\/tspan><\/text>\n<line x1=\"459.3\" y1=\"165\" x2=\"459.3\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"459.3\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">5<\/tspan><\/text>\n<line x1=\"560.7\" y1=\"165\" x2=\"560.7\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"560.7\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">15<\/tspan><\/text>\n<line x1=\"662.0\" y1=\"165\" x2=\"662.0\" y2=\"175\" stroke=\"#C5D0DC\" stroke-width=\"1\"><\/line>\n<text x=\"662.0\" y=\"192\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">10<tspan font-size=\"9\" dy=\"-5\">25<\/tspan><\/text>\n<line x1=\"72.5\" y1=\"166\" x2=\"72.5\" y2=\"146\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"72.5\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"72.5\" y=\"140\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">h<\/text>\n<line x1=\"177.0\" y1=\"166\" x2=\"177.0\" y2=\"112\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"177.0\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"177.0\" y=\"106\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">k<\/text>\n<line x1=\"305.6\" y1=\"166\" x2=\"305.6\" y2=\"78\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"305.6\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"305.6\" y=\"72\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">G<\/text>\n<line x1=\"418.0\" y1=\"166\" x2=\"418.0\" y2=\"146\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"418.0\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"418.0\" y=\"140\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">R<\/text>\n<line x1=\"418.7\" y1=\"166\" x2=\"418.7\" y2=\"112\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"418.7\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"418.7\" y=\"106\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">g<\/text>\n<line x1=\"434.4\" y1=\"166\" x2=\"434.4\" y2=\"78\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"434.4\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"434.4\" y=\"72\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">v<\/text>\n<line x1=\"494.6\" y1=\"166\" x2=\"494.6\" y2=\"146\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"494.6\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"494.6\" y=\"140\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">c<\/text>\n<line x1=\"509.5\" y1=\"166\" x2=\"509.5\" y2=\"112\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"509.5\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"509.5\" y=\"106\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">k<tspan font-size=\"10\" dy=\"3\">e<\/tspan><\/text>\n<line x1=\"649.6\" y1=\"166\" x2=\"649.6\" y2=\"78\" stroke=\"#C8932A\" stroke-width=\"1\" opacity=\"0.55\"><\/line>\n<circle cx=\"649.6\" cy=\"170\" r=\"4\" fill=\"#C8932A\"><\/circle>\n<text x=\"649.6\" y=\"72\" text-anchor=\"middle\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#FAF6EE\">N<tspan font-size=\"10\" dy=\"3\">A<\/tspan><\/text>\n<text x=\"24\" y=\"236\" font-family=\"Manrope,Segoe UI,Arial,sans-serif\" font-size=\"11\" fill=\"#C5D0DC\">From the Planck constant near 10<tspan font-size=\"9\" dy=\"-4\">-34<\/tspan><tspan dy=\"4\"> to the Avogadro constant near 10<\/tspan><tspan font-size=\"9\" dy=\"-4\">24<\/tspan><tspan dy=\"4\">.<\/tspan><\/text>\n<\/svg>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">Physics constants plotted on a logarithmic scale, from the Planck constant to the Avogadro constant.<\/p>\n\n<p>A useful sanity check follows from that picture: if a calculation involving h returns something near 1, you have almost certainly dropped a power of ten somewhere.<\/p>\n\n<h2>Real-World Examples of Physics Constants at Work<\/h2>\n\n<p>Physics constants are not confined to exam papers; they are wired into technology you use daily. Five cases make the point.<\/p>\n\n<ul>\n<li><strong>Satellite navigation (c).<\/strong> Your position is worked out from signal travel times. Light covers about 30 cm in a nanosecond, so a clock error of a few nanoseconds becomes a metre of error on the ground.<\/li>\n<li><strong>LED lighting and screens (h).<\/strong> The colour of an LED is set by the photon energy it emits. A blue LED at 450 nm puts out photons of about 2.76 eV, and h is the conversion factor that gets you there.<\/li>\n<li><strong>Kitchen and laboratory scales (g).<\/strong> A scale measures force, then divides by g to display a mass. Ship the same scale from the equator to the Arctic without recalibrating and a 70 kg reading drifts by roughly 0.36 kg.<\/li>\n<li><strong>Tyre pressure and weather balloons (R).<\/strong> Both are the ideal gas law in disguise: warm the gas and either the pressure or the volume has to give.<\/li>\n<li><strong>Judging a thunderstorm (v).<\/strong> Count the seconds between flash and bang. Three seconds at 343 m\/s puts the strike about a kilometre away.<\/li>\n<\/ul>\n\n<h2>Common Misconceptions About Physics Constants<\/h2>\n\n<p>Four errors account for most of the marks lost on this topic, and the first is by far the most expensive.<\/p>\n\n<h3>Mistake 1: Treating g and G as the Same Thing<\/h3>\n\n<p>They are different quantities with different units and different natures. G is a universal constant in m\u00b3 kg<sup>-1<\/sup> s<sup>-2<\/sup>; g is a local field strength in N\/kg that changes depending on where you stand.<\/p>\n\n<p>The two connect only through a specific body: g = GM\/R\u00b2, where M and R are that planet&#8217;s mass and radius. Confusing them also feeds the older confusion between <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/weight-vs-mass\/\">weight and mass<\/a>, since weight is the thing that changes when g does.<\/p>\n\n<h3>Mistake 2: Assuming g Is 9.81 Everywhere<\/h3>\n\n<p>Local gravity varies by about half a percent across Earth&#8217;s surface, from roughly 9.78 m\/s\u00b2 at the equator to 9.83 m\/s\u00b2 near the poles. Altitude and local rock density shift it further.<\/p>\n\n<p>Use 9.81 m\/s\u00b2 as a working value, but do not report an answer to five significant figures on the back of it.<\/p>\n\n<h3>Mistake 3: Thinking c Is Still Being Measured More Precisely<\/h3>\n\n<p>It is not, and it cannot be. Since 1983 the metre has been <em>defined<\/em> from the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/modern-physics\/speed-of-light\/\">speed of light<\/a>, so measuring c more accurately now just measures your ruler.<\/p>\n\n<p>Any experiment that appears to time light more precisely is really calibrating a length standard.<\/p>\n\n<h3>Mistake 4: Treating R and k as Unrelated<\/h3>\n\n<p>They are the same physics at two different scales. The Boltzmann constant k applies per particle, the gas constant R applies per mole, and R = N<sub>A<\/sub>k connects them exactly.<\/p>\n\n<p>Use R when you are counting in moles and k when you are counting individual molecules \u2014 mixing them up is a factor of 6 \u00d7 10<sup>23<\/sup> error, which is hard to miss.<\/p>\n\n<h2>How Physics Constants Relate to Formulas, Units and Uncertainty<\/h2>\n\n<p>A constant only means something once it is attached to an equation and a set of units. That is why this page pairs naturally with the wider toolkit.<\/p>\n\n<ul>\n<li><strong>Formulas.<\/strong> Every constant here is the fixed term in some relationship; the grouped guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/physics-formulas\/\">physics formulas<\/a> shows where each one slots in.<\/li>\n<li><strong>Thermodynamics.<\/strong> R does its main work in the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/ideal-gas-law\/\">ideal gas law<\/a>, where keeping temperature in kelvin is the whole battle.<\/li>\n<li><strong>Quantum physics.<\/strong> h is the bridge between frequency and energy, worked through step by step in the guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/modern-physics\/photon-energy-formula\/\">photon energy<\/a>.<\/li>\n<li><strong>Electrostatics.<\/strong> k<sub>e<\/sub> exists only inside <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/coulombs-law\/\">Coulomb&#8217;s law<\/a>, and its enormous size is why static shocks are so easy to generate.<\/li>\n<\/ul>\n\n<p>Uncertainty is the thread running through all of it. Your answer can never be more precise than the least precise number you fed in, and with gravity that number is almost always G.<\/p>\n\n<h2>Worked Problems<\/h2>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A student has a mass of 72 kg. Calculate their weight on Earth, taking g = 9.81 m\/s\u00b2.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Weight is the gravitational force on a mass, W = mg.\nStep 2: Substitute with units. W = 72 kg \u00d7 9.81 m\/s<sup>2<\/sup> = 72 \u00d7 9.81 kg m\/s<sup>2<\/sup>.\nStep 3: Solve. W = 706.32 N, and 1 kg m\/s<sup>2<\/sup> is 1 N.\n<strong>Answer: W = 706 N (3 s.f.)<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">The Sun is 1.496 x 10^11 m from Earth. How long does its light take to reach us?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Light travels at constant speed in vacuum, so t = d \/ c.\nStep 2: Substitute with units. t = (1.496 \u00d7 10<sup>11<\/sup> m) \/ (2.99792458 \u00d7 10<sup>8<\/sup> m\/s).\nStep 3: Solve. t = 499.0 s, and 499.0 \/ 60 = 8.32 min.\n<strong>Answer: t = 499 s, or about 8.32 minutes<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">On a day when the air temperature is 35 \u00b0C, thunder arrives 4.2 s after the flash. How far away was the strike?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Find the speed of sound at that temperature using v = 331.3 sqrt(1 + T\/273.15).\nStep 2: Substitute. v = 331.3 \u00d7 sqrt(1 + 35\/273.15) = 331.3 \u00d7 sqrt(1.1281) = 351.9 m\/s.\nStep 3: Distance is d = vt = 351.9 m\/s \u00d7 4.2 s = 1478 m.\n<strong>Answer: d = 1.5 km (2 s.f.)<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">Green light has a wavelength of 500 nm. Calculate the energy of one photon in joules and in electronvolts.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Get the frequency from f = c \/ \u03bb, then use E = hf.\nStep 2: f = (2.99792458 \u00d7 10<sup>8<\/sup> m\/s) \/ (500 \u00d7 10<sup>-9<\/sup> m) = 5.996 \u00d7 10<sup>14<\/sup> Hz.\nStep 3: E = (6.62607015 \u00d7 10<sup>-34<\/sup> J s) \u00d7 (5.996 \u00d7 10<sup>14<\/sup> Hz) = 3.973 \u00d7 10<sup>-19<\/sup> J.\nStep 4: Convert using 1 eV = 1.602176634 \u00d7 10<sup>-19<\/sup> J, giving 3.973 \/ 1.602 = 2.48 eV.\n<strong>Answer: E = 3.97 \u00d7 10<sup>-19<\/sup> J, or 2.48 eV<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">Calculate the volume occupied by 1.00 mol of an ideal gas at 273.15 K and 101,325 Pa.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Rearrange the ideal gas law pV = nRT to give V = nRT \/ p.\nStep 2: Substitute with units. V = (1.00 mol \u00d7 8.314462618 J mol<sup>-1<\/sup> K<sup>-1<\/sup> \u00d7 273.15 K) \/ 101,325 Pa.\nStep 3: The numerator is 2271.0 J, so V = 2271.0 \/ 101,325 = 0.022414 m<sup>3<\/sup>.\nStep 4: Convert to litres: 0.022414 m<sup>3<\/sup> \u00d7 1000 = 22.41 L.\n<strong>Answer: V = 0.02241 m<sup>3<\/sup>, or 22.41 L<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">Earth has mass 5.972 x 10^24 kg and mean radius 6.371 x 10^6 m. Use G to calculate g at its surface, and comment on the result.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Surface field strength comes from g = GM \/ R<sup>2<\/sup>.\nStep 2: Numerator: (6.67430 \u00d7 10<sup>-11<\/sup>) \u00d7 (5.972 \u00d7 10<sup>24<\/sup>) = 3.986 \u00d7 10<sup>14<\/sup>.\nStep 3: Denominator: (6.371 \u00d7 10<sup>6<\/sup>)<sup>2<\/sup> = 4.059 \u00d7 10<sup>13<\/sup>.\nStep 4: g = 3.986 \u00d7 10<sup>14<\/sup> \/ 4.059 \u00d7 10<sup>13<\/sup> = 9.82 m\/s<sup>2<\/sup>.\nStep 5: This sits just above the conventional 9.81 m\/s<sup>2<\/sup> because the calculation ignores Earth&#8217;s rotation and its equatorial bulge.\n<strong>Answer: g = 9.82 m\/s<sup>2<\/sup>, confirming that g is derived from G, not independent of it<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">Two 1.0 \u03bcC charges sit 1.0 cm apart. Two 1.0 kg masses sit 1.0 cm apart. Compare the electrostatic and gravitational forces.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Electrostatic force, F = k<sub>e<\/sub> q<sub>1<\/sub> q<sub>2<\/sub> \/ r<sup>2<\/sup>.\nStep 2: F<sub>E<\/sub> = (8.98755 \u00d7 10<sup>9<\/sup>) \u00d7 (1.0 \u00d7 10<sup>-6<\/sup>)<sup>2<\/sup> \/ (0.010)<sup>2<\/sup> = (8.98755 \u00d7 10<sup>9<\/sup> \u00d7 10<sup>-12<\/sup>) \/ 10<sup>-4<\/sup> = 89.9 N.\nStep 3: Gravitational force, F = G m<sub>1<\/sub> m<sub>2<\/sub> \/ r<sup>2<\/sup>.\nStep 4: F<sub>G<\/sub> = (6.67430 \u00d7 10<sup>-11<\/sup>) \u00d7 (1.0) \u00d7 (1.0) \/ (0.010)<sup>2<\/sup> = 6.674 \u00d7 10<sup>-7<\/sup> N.\nStep 5: Ratio = 89.9 \/ (6.674 \u00d7 10<sup>-7<\/sup>) = 1.35 \u00d7 10<sup>8<\/sup>.\n<strong>Answer: The electrostatic force is about 1.3 \u00d7 10<sup>8<\/sup> times larger<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 8<\/div><div class=\"pf-problem-question\">A photon carries 2.00 eV of energy. Find its wavelength in nanometres using the product hc.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong>\nStep 1: Combine E = hf and c = f \u03bb to get \u03bb = hc \/ E.\nStep 2: Work out hc once. hc = (6.62607015 \u00d7 10<sup>-34<\/sup> J s) \u00d7 (2.99792458 \u00d7 10<sup>8<\/sup> m\/s) = 1.9864 \u00d7 10<sup>-25<\/sup> J m.\nStep 3: Convert to convenient units: divide by 1.602176634 \u00d7 10<sup>-19<\/sup> J\/eV and multiply by 10<sup>9<\/sup> nm\/m, giving hc = 1240 eV nm.\nStep 4: \u03bb = 1240 eV nm \/ 2.00 eV = 620 nm.\n<strong>Answer: \u03bb = 620 nm, in the orange-red part of the visible spectrum<\/strong>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What are the physics constants?<\/summary><div class=\"pf-faq-item-answer\">\nPhysics constants are fixed quantities that appear in the laws of physics and keep the same value everywhere. The core set includes the speed of light c, the Planck constant h, the gravitational constant G, the molar gas constant R, the Boltzmann constant k and the Avogadro constant. Standard gravity g is usually listed with them, though it is a conventional value rather than a universal one.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is g the same as G?<\/summary><div class=\"pf-faq-item-answer\">\nNo. G is the universal gravitational constant, 6.67430 \u00d7 10<sup>-11<\/sup> m<sup>3<\/sup> kg<sup>-1<\/sup> s<sup>-2<\/sup>, and it is the same throughout the universe. Lowercase g is the local gravitational field strength, about 9.81 N\/kg at Earth&#8217;s surface, and it changes with location and with which planet you are on. They are linked by g = GM\/R<sup>2<\/sup>.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Which physics constants are exact?<\/summary><div class=\"pf-faq-item-answer\">\nFive are exact because the SI defines them: the speed of light, the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant. Constants built purely from these, such as the molar gas constant R and the Stefan-Boltzmann constant, are exact too. The gravitational constant G is measured, and is known only to about 22 parts per million.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the value of Planck&#039;s constant?<\/summary><div class=\"pf-faq-item-answer\">\nThe Planck constant is exactly 6.62607015 \u00d7 10<sup>-34<\/sup> joule seconds. Since May 2019 this value has been fixed by definition and carries no uncertainty, because it is what now defines the kilogram. The reduced Planck constant, written h-bar, is h divided by 2 \u03c0 and equals 1.054571817 \u00d7 10<sup>-34<\/sup> J s.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why is the speed of light exactly 299,792,458 m\/s?<\/summary><div class=\"pf-faq-item-answer\">\nBecause the metre is defined from it. In 1983 the metre was redefined as the distance light travels in vacuum in 1\/299,792,458 of a second, which fixed c at that value permanently. The number itself is a historical accident, chosen so the new metre matched the old one as closely as possible.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Do physics constants change over time?<\/summary><div class=\"pf-faq-item-answer\">\nThere is no experimental evidence that they do. Astronomers have compared spectra from distant quasars with laboratory measurements and found no drift in the fine-structure constant at current precision. Constants defined by the SI, such as c and h, cannot change at all, since their values are fixed by agreement rather than measured.\n<\/div><\/details>\n\n<h2>Key Takeaways<\/h2>\n\n<ul>\n<li>Physics constants split into exact defining values, exact derived values, measured values, and conventional or conditional values.<\/li>\n<li>c, h, e, k and the Avogadro constant are exact by definition, and together with two others they now define every SI base unit.<\/li>\n<li>G is the least precisely known constant here, at about 22 parts per million.<\/li>\n<li>Lowercase g is not a universal constant; it varies from roughly 9.78 to 9.83 m\/s^2 across Earth&#8217;s surface.<\/li>\n<li>Always carry units through the algebra, and never report more significant figures than your least precise constant allows.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A complete reference to the physics constants used in school and first-year university physics, with exact CODATA 2022 values, SI units and worked examples. Covers g, c, h, G, R, the Coulomb constant and the speed of sound, and explains which are exact and which are measured.<\/p>\n","protected":false},"author":1,"featured_media":692,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-690","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanics"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/690","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=690"}],"version-history":[{"count":1,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/690\/revisions"}],"predecessor-version":[{"id":693,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/690\/revisions\/693"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/692"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=690"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=690"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=690"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}