{"id":763,"date":"2026-08-10T23:55:49","date_gmt":"2026-08-10T23:55:49","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=763"},"modified":"2026-08-24T13:03:46","modified_gmt":"2026-08-24T13:03:46","slug":"physics-unit-conversions","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/physics-unit-conversions\/","title":{"rendered":"Physics Unit Conversions: N, J, Pa, K and More"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nPhysics unit conversions rewrite a measured quantity in different units without changing the quantity itself. You multiply by a conversion ratio \u2014 a fraction equal to 1, such as 1000 m \/ 1 km \u2014 so the unwanted unit cancels. Temperature is the exception: kelvin and degrees Celsius are separated by an additive offset of 273.15, not a factor.\n<\/p><\/div>\n\n<p>Your car manual specifies 2.2 bar. The garage gauge reads psi. The tyre itself is stamped in kPa. Three numbers, three units, one physical quantity \u2014 and somewhere in that gap, people guess.<\/p>\n\n<p>Physics runs on the same gap, only the stakes are higher. A joule and an electronvolt both measure energy, but they differ by nineteen orders of magnitude. Get the factor wrong and your answer is not slightly off; it is meaningless.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/Mars_Climate_Orbiter_2.jpg\"\n\n       alt=\"Mars Climate Orbiter, lost in 1999 to a physics unit conversions error\"\n\n       loading=\"lazy\"\n\n       style=\"width:100%;height:auto;border-radius:4px;\" width=\"1920\" height=\"1745\">\n\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">NASA lost the Mars Climate Orbiter in 1999 after ground software reported thruster impulse in pound-force seconds where the specification required newton-seconds.<\/figcaption>\n\n<\/figure>\n\n<h2>What Are Physics Unit Conversions?<\/h2>\n\n<p>A unit conversion changes the <em>label<\/em> on a measurement, never the measurement. Write 5 kg or 5000 g and you are describing the same lump of matter; only the yardstick changed.<\/p>\n\n<p>That sounds obvious until you meet a unit that hides a second quantity inside it. A newton is not a fundamental thing \u2014 it is shorthand for kg\u00b7m\/s<sup>2<\/sup>. An electronvolt smuggles in the elementary charge. A pascal is a newton spread over a square metre.<\/p>\n\n<p>So conversions come in two flavours, and confusing them is where marks go missing:<\/p>\n\n<ul>\n<li><strong>Scale conversions<\/strong> \u2014 multiply by a factor. Nearly everything: N to kN, J to eV, Pa to atm, m to miles.<\/li>\n<li><strong>Affine conversions<\/strong> \u2014 multiply <em>and<\/em> shift. Only temperature scales that do not start at absolute zero, namely degrees Celsius and degrees Fahrenheit.<\/li>\n<\/ul>\n\n<p>Everything else in this guide follows from knowing which one you are holding.<\/p>\n\n<h2>The Conversion-Ratio Method: One Rule Behind Every Conversion<\/h2>\n\n<p>Every scale conversion is a multiplication by a fraction that equals exactly 1. Because 1000 m and 1 km are the same length, the fraction 1000 m \/ 1 km has the value 1 \u2014 so multiplying by it changes the units on the page without touching the physical quantity.<\/p>\n\n<div class=\"pf-formula\">value in new units = value in old units x (new unit per old unit)<\/div>\n\n<p>Written as a chain, the units behave like algebra: anything appearing top and bottom cancels, and you keep multiplying ratios until only the unit you want survives.<\/p>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/physics-unit-conversions-conversion-ratio-method-converting-108.webp\" width=\"1400\" height=\"560\" alt=\"Physics unit conversions - Diagram of the conversion-ratio method converting 108 kilometres per hour to 30 metres per second by cancelling units\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:0 auto;\" \/><\/figure>\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">The conversion-ratio method: stack fractions worth 1 until the unwanted units cancel.<\/p>\n\n<p>Two habits make this reliable. Carry the units through every line rather than tracking numbers alone, and keep full precision until the very end \u2014 <a href=\"https:\/\/www.nist.gov\/pml\/owm\/metric-si\/unit-conversion\" target=\"_blank\" rel=\"noopener\">NIST&#8217;s guidance on unit conversion<\/a> is explicit that you round once, on the final answer.<\/p>\n\n<p>In practice, the cancelling is also your error-check. If you finish a chain and the leftover units are not the ones you wanted, you have flipped a ratio upside down \u2014 no need to hunt through the arithmetic.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Unit Conversions 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\/unit-conversions.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>SI Prefixes: The Conversions You Do Most Often<\/h2>\n\n<p>Prefix conversions are pure powers of ten, which is why they feel easy and get botched anyway. The prefix is part of the unit, so &#8220;k&#8221; always means the number 1000 sitting in front of whatever follows.<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Prefix<\/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;\">Factor<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Typical physics use<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">tera<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">T<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>12<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">THz optical frequencies<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">giga<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">G<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>9<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">GeV particle energies<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">mega<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">M<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>6<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">MPa material stress<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">kilo<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">k<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>3<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">kN forces, kJ energies<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">centi<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">c<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-2<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">cm lengths, cm<sup>3<\/sup> volumes<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">milli<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">m<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-3<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">mA currents, mm lengths<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">micro<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">\u03bc<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-6<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">\u03bcF capacitance<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">nano<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">n<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-9<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">nm wavelengths<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">pico<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">p<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-12<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">pF capacitance<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">femto<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">f<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-15<\/sup><\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">fm nuclear radii<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>The trap is prefixes on squared and cubed units, because the exponent hits the prefix too. Since 1 cm = 10<sup>-2<\/sup> m, it follows that 1 cm<sup>3<\/sup> = (10<sup>-2<\/sup> m)<sup>3<\/sup> = 10<sup>-6<\/sup> m<sup>3<\/sup> \u2014 a factor of a million, not a hundred.<\/p>\n\n<p>That single slip is behind most density errors, which is why 1 g\/cm<sup>3<\/sup> equals 1000 kg\/m<sup>3<\/sup> rather than anything smaller. If you would rather not do the powers by hand, our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/si-prefix-converter\">SI Prefix Converter<\/a> steps a value between any two prefixes and shows the exponent arithmetic.<\/p>\n\n<h2>Force Conversions: N, kN, dyne and Pound-Force<\/h2>\n\n<p>The newton is the SI unit of force, defined as the force that accelerates 1 kg at 1 m\/s<sup>2<\/sup>. Everything in the table below is that same quantity wearing a different coat.<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Unit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Value in newtons<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Exact?<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Where you meet it<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 kilonewton (kN)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1000 N<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Structural loads, rocket thrust<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 millinewton (mN)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">0.001 N<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Ion thrusters, surface tension<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 dyne (dyn)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-5<\/sup> N<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Older CGS-unit papers<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 kilogram-force (kgf)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">9.80665 N<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Engineering, gym plates<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 pound-force (lbf)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">4.4482 N<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">4.448 221 615 260 5 N exactly<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">US aerospace and engineering<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Notice that the pound-force factor is exact rather than measured. It falls out of two defined numbers: the pound is exactly 0.453 592 37 kg, and standard gravity is exactly 9.806 65 m\/s<sup>2<\/sup>.<\/p>\n\n<p>Which raises the single most common force error. Kilograms measure mass; newtons measure force. On Earth a 1 kg mass <em>weighs<\/em> about 9.81 N, but that is a physics calculation using <em>g<\/em>, not a unit conversion \u2014 and the answer changes on the Moon while the mass does not. If that distinction feels shaky, our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/types-of-forces\/\">the types of forces in physics<\/a> works through weight as a force in detail.<\/p>\n\n<h2>Energy Conversions: J, eV, Calories and Kilowatt-Hours<\/h2>\n\n<p>Energy has the messiest unit zoo in physics, because chemists, electricians, nutritionists and particle physicists all invented their own. The joule ties them together: 1 J = 1 N\u00b7m = 1 kg\u00b7m<sup>2<\/sup>\/s<sup>2<\/sup>.<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Unit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Value in joules<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Exact?<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Where you meet it<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 electronvolt (eV)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1.602 176 634 x 10<sup>-19<\/sup> J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact since 2019<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Atomic and particle physics<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 erg<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">10<sup>-7<\/sup> J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Astrophysics, CGS papers<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 calorie (thermochemical)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">4.184 J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Calorimetry, chemistry<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 food Calorie (kcal)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">4184 J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Nutrition labels<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 foot pound-force (ft\u00b7lbf)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1.355 82 J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact to more digits<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">US mechanical work<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 BTU (international table)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1055.055 852 62 J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Heating and cooling ratings<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 kilowatt-hour (kWh)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">3.6 x 10<sup>6<\/sup> J<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Electricity bills<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>The electronvolt deserves a second look, because it is defined rather than measured. Since the 2019 redefinition fixed the elementary charge at exactly 1.602 176 634 x 10<sup>-19<\/sup> C, the eV-to-joule factor is now exact by construction.<\/p>\n\n<p>Going the other way, 1 J = 6.241 509 074 x 10<sup>18<\/sup> eV. That vast ratio is precisely why nobody quotes a photon in joules \u2014 a visible photon carries a few eV, and writing it as 0.000 000 000 000 000 000 4 J helps no one. For the underlying concept, see our explainer on <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-energy-in-physics\/\">what energy is in physics<\/a>.<\/p>\n\n<p>One warning on calories. The &#8220;calorie&#8221; on a food label is a kilocalorie \u2014 1000 thermochemical calories \u2014 so a 250 Calorie snack is 250 kcal, or roughly 1.05 x 10<sup>6<\/sup> J.<\/p>\n\n<h2>Pressure Conversions: Pa, kPa, atm, bar and psi<\/h2>\n\n<p>The pascal is one newton per square metre, which makes it a remarkably small unit. Atmospheric pressure is about 101 000 Pa, so real-world pressures almost always appear with a prefix or in a legacy unit.<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Unit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Value in pascals<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Exact?<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Where you meet it<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 kilopascal (kPa)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1000 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Tyre placards, weather<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 bar<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">100 000 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Meteorology, diving<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 standard atmosphere (atm)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">101 325 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Gas laws, chemistry<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 torr<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">133.322 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exactly 101 325\/760 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Vacuum systems<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 mmHg (conventional)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">133.322 387 415 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Blood pressure, barometry<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 psi (lbf\/in<sup>2<\/sup>)<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">6894.76 Pa<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Exact to more digits<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">Tyres, US engineering<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Note that 1 bar and 1 atm are close but not equal \u2014 1 atm is 1.013 25 bar. Treating them as identical introduces a 1.3% error, which is fine for a rough estimate and fatal in a gas-law calculation.<\/p>\n\n<p>Torr and mmHg are a second near-miss. Torr is defined as exactly one seven-hundred-and-sixtieth of an atmosphere, while the conventional millimetre of mercury is defined from a fixed mercury density \u2014 they agree to about one part in ten million. For the underlying physics, see our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/fluids\/pressure-in-physics\/\">pressure in physics<\/a>.<\/p>\n\n<h2>Temperature Conversions: K, \u00b0C and \u00b0F, Where the Rule Changes<\/h2>\n\n<p>Temperature is the one place the conversion-ratio method fails, because the Celsius and Fahrenheit scales do not put zero at absolute zero. You must shift as well as scale.<\/p>\n\n<div class=\"pf-formula\">T(K) = t(\u00b0C) + 273.15<\/div>\n\n<div class=\"pf-formula\">t(\u00b0F) = (9\/5) x t(\u00b0C) + 32<\/div>\n\n<div class=\"pf-formula\">T(K) = (t(\u00b0F) + 459.67) x 5\/9<\/div>\n\n<ul>\n<li><strong>T<\/strong> \u2014 thermodynamic temperature, unit kelvin (K)<\/li>\n<li><strong>t<\/strong> \u2014 Celsius or Fahrenheit temperature, unit degree Celsius (\u00b0C) or degree Fahrenheit (\u00b0F)<\/li>\n<li><strong>273.15<\/strong> \u2014 the exact offset between the kelvin and Celsius scales<\/li>\n<\/ul>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/physics-unit-conversions-comparison-kelvin-celsius-fahrenheit-temperatur.webp\" width=\"1400\" height=\"680\" alt=\"Physics unit conversions - Comparison of kelvin, Celsius and Fahrenheit temperature scales showing absolute zero, water freezing and water boiling points\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:0 auto;\" \/><\/figure>\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">The 273.15 offset between kelvin and Celsius, and why Fahrenheit needs a factor as well as a shift.<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Reference point<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Kelvin (K)<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Celsius (\u00b0C)<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Fahrenheit (\u00b0F)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">Absolute zero<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">0<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">-273.15<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">-459.67<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">Water freezes<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">273.15<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">0<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">32<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">Room temperature<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">293.15<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">20<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">68<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">Body temperature<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">310.15<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">37<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">98.6<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">Water boils<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">373.15<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">100<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">212<\/td><\/tr>\n<tr><td style=\"padding:8px;border:1px solid #D9CFB8;\">An interval of 1 degree<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 K<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1 \u00b0C<\/td><td style=\"padding:8px;border:1px solid #D9CFB8;\">1.8 \u00b0F<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<h3>Readings shift, but differences do not<\/h3>\n\n<p>Here is the subtlety that separates a confident answer from a lucky one. A <em>reading<\/em> of 25 \u00b0C converts to 298.15 K, but a <em>rise<\/em> of 25 \u00b0C is a rise of exactly 25 K \u2014 no offset at all.<\/p>\n\n<p>The reason is that the offset cancels when you subtract two temperatures. So in any formula containing \u0394T, such as Q = mc\u0394T, you may use Celsius and kelvin interchangeably. Our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/heat-vs-temperature\/\">heat versus temperature<\/a> unpacks why that distinction matters physically.<\/p>\n\n<p>Absolute temperatures are a different story. Anything with T alone \u2014 the ideal gas law, Stefan-Boltzmann, Carnot efficiency \u2014 needs kelvin, because a scale that can go negative would let you compute negative pressures and impossible efficiencies.<\/p>\n\n<h2>Common Misconceptions About Physics Unit Conversions<\/h2>\n\n<h3>&#8220;You write degrees kelvin, \u00b0K&#8221;<\/h3>\n\n<p>No \u2014 the correct symbol is K, with no degree sign and no &#8220;degrees&#8221; in speech. The 13th General Conference on Weights and Measures dropped &#8220;degree Kelvin&#8221; in favour of the kelvin, as <a href=\"https:\/\/www.bipm.org\/en\/history-si\/kelvin\" target=\"_blank\" rel=\"noopener\">BIPM&#8217;s history of the kelvin<\/a> records. It is 300 K, read aloud as &#8220;three hundred kelvin&#8221;.<\/p>\n\n<h3>&#8220;Converting kg to N is a unit conversion&#8221;<\/h3>\n\n<p>It is not. Kilograms measure mass and newtons measure force, so no conversion ratio connects them. Multiplying by <em>g<\/em> is a physics step that answers a different question \u2014 what does this mass weigh, here?<\/p>\n\n<h3>&#8220;Just use 273 instead of 273.15&#8221;<\/h3>\n\n<p>Rounding the offset costs you about 0.05%, which sounds harmless and quietly wrecks precision work. In a gas-law problem at 300 K, that is a 0.15 K error carried into every subsequent line \u2014 and it is free to avoid.<\/p>\n\n<h3>&#8220;A prefix on a squared unit still means the same power of ten&#8221;<\/h3>\n\n<p>The exponent applies to the whole unit, prefix included. So 1 m<sup>2<\/sup> = 10 000 cm<sup>2<\/sup>, not 100 \u2014 and 1 m<sup>3<\/sup> = 1 000 000 cm<sup>3<\/sup>. Sanity-check by asking whether the number moved in the direction you expected.<\/p>\n\n<h2>How Unit Conversions Relate to SI Units, Constants and Dimensional Analysis<\/h2>\n\n<p>Conversions sit on top of the SI system rather than beside it. Every derived unit decomposes into the seven base units, which is why a joule can be rewritten as kg\u00b7m<sup>2<\/sup>\/s<sup>2<\/sup> and a pascal as kg\/(m\u00b7s<sup>2<\/sup>) \u2014 our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/si-units-physics\/\">SI units in physics<\/a> covers that structure in full.<\/p>\n\n<p>That decomposition gives you a free check on any equation. If you reduce both sides to base units and they disagree, the equation is wrong \u2014 no arithmetic required. Dimensional analysis catches an inverted conversion ratio faster than re-checking the numbers ever will.<\/p>\n\n<p>Constants tie the same knot. Many are quoted in more than one unit system, and picking the wrong one silently rescales your answer; our <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/physics-constants\/\">table of physics constants<\/a> lists them with the units attached, which is the safest way to store them.<\/p>\n\n<p>For exact factors beyond the ones tabulated here, <a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" target=\"_blank\" rel=\"noopener\">NIST Special Publication 811, Appendix B<\/a> is the reference to keep bookmarked. It marks which factors are exact by definition and which have been rounded.<\/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 crane cable carries a tension of 24 500 N. Express this force in kilonewtons.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: The prefix kilo means 10<sup>3<\/sup>, so 1 kN = 1000 N. The conversion ratio is 1 kN \/ 1000 N.<\/p>\n<p>Step 2: 24 500 N x (1 kN \/ 1000 N) = 24 500 \/ 1000 kN.<\/p>\n<p>Step 3: The unit N cancels top and bottom, leaving kN.<\/p>\n<p><strong>Answer: 24.5 kN<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">A car travels at 108 km\/h. Convert this speed to metres per second.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Two ratios are needed, one for length and one for time: 1000 m \/ 1 km and 1 h \/ 3600 s.<\/p>\n<p>Step 2: 108 km\/h x (1000 m \/ 1 km) x (1 h \/ 3600 s) = (108 x 1000) \/ 3600 m\/s.<\/p>\n<p>Step 3: 108 000 \/ 3600 = 30. Both km and h cancel, leaving m\/s.<\/p>\n<p><strong>Answer: 30.0 m\/s<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A gas sample is at 27 \u00b0C. What is its thermodynamic temperature in kelvin?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: This is an absolute temperature, so use T(K) = t(\u00b0C) + 273.15.<\/p>\n<p>Step 2: T = 27 + 273.15.<\/p>\n<p>Step 3: T = 300.15 K. Note that no multiplication appears \u2014 the scales share a step size.<\/p>\n<p><strong>Answer: 300.15 K<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">Iron has a density of 7.87 g\/cm^3. Express this density in kg\/m^3.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Convert mass and volume separately: 1 kg \/ 1000 g, and 1 cm<sup>3<\/sup> = 10<sup>-6<\/sup> m<sup>3<\/sup>, so the volume ratio is 10<sup>6<\/sup> cm<sup>3<\/sup> \/ 1 m<sup>3<\/sup>.<\/p>\n<p>Step 2: 7.87 g\/cm<sup>3<\/sup> x (1 kg \/ 1000 g) x (10<sup>6<\/sup> cm<sup>3<\/sup> \/ 1 m<sup>3<\/sup>) = 7.87 x 10<sup>6<\/sup> \/ 1000 kg\/m<sup>3<\/sup>.<\/p>\n<p>Step 3: 7.87 x 1000 = 7870. The cube on cm brought in 10<sup>6<\/sup>, not 10<sup>2<\/sup>.<\/p>\n<p><strong>Answer: 7870 kg\/m<sup>3<\/sup><\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">A photon of green light carries 2.50 eV of energy. Convert this to joules.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Use the exact defined factor 1 eV = 1.602 176 634 x 10<sup>-19<\/sup> J.<\/p>\n<p>Step 2: E = 2.50 eV x (1.602 176 634 x 10<sup>-19<\/sup> J \/ 1 eV).<\/p>\n<p>Step 3: E = 4.005 441 585 x 10<sup>-19<\/sup> J, rounded to the 3 significant figures of the input.<\/p>\n<p><strong>Answer: 4.01 x 10<sup>-19<\/sup> J<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A sealed vessel is at 2.50 atm. Express this pressure in pascals and in kilopascals.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: By definition 1 atm = 101 325 Pa exactly.<\/p>\n<p>Step 2: P = 2.50 atm x (101 325 Pa \/ 1 atm) = 253 312.5 Pa.<\/p>\n<p>Step 3: Rounding to 3 significant figures gives 2.53 x 10<sup>5<\/sup> Pa, and dividing by 1000 gives kPa.<\/p>\n<p><strong>Answer: 2.53 x 10<sup>5<\/sup> Pa, or 253 kPa<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">A household appliance uses 2.4 kWh of electrical energy. How many joules is this?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: A watt is a joule per second, so 1 kWh = 1000 W x 3600 s = 3.6 x 10<sup>6<\/sup> J.<\/p>\n<p>Step 2: E = 2.4 kWh x (3.6 x 10<sup>6<\/sup> J \/ 1 kWh).<\/p>\n<p>Step 3: E = 8.64 x 10<sup>6<\/sup> J.<\/p>\n<p><strong>Answer: 8.64 x 10<sup>6<\/sup> J (8.64 MJ)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 8<\/div><div class=\"pf-problem-question\">The specific heat capacity of water is often quoted as 1.00 cal\/(g\u00b7\u00b0C). Convert this to SI units of J\/(kg\u00b7K).<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Three ratios are needed: 4.184 J \/ 1 cal, 1000 g \/ 1 kg, and the interval identity 1 \u00b0C = 1 K.<\/p>\n<p>Step 2: The \u00b0C here is a temperature <em>difference<\/em>, not a reading, so no 273.15 offset applies \u2014 the degree simply becomes a kelvin.<\/p>\n<p>Step 3: 1.00 x (4.184 J \/ 1 cal) x (1000 g \/ 1 kg) = 4184 J\/(kg\u00b7K).<\/p>\n<p><strong>Answer: 4184 J\/(kg\u00b7K), or 4.18 x 10<sup>3<\/sup> J\/(kg\u00b7K) to 3 significant figures<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>How do you convert N to kN?<\/summary><div class=\"pf-faq-item-answer\">\nDivide the number of newtons by 1000. The prefix kilo means 10<sup>3<\/sup>, so 1 kN = 1000 N and 24 500 N becomes 24.5 kN. Going the other way, multiply by 1000. Because this is a pure power of ten, the conversion is exact and the significant figures of your original value are unchanged.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why do you add 273.15 to convert Celsius to kelvin?<\/summary><div class=\"pf-faq-item-answer\">\nBecause the two scales use the same size of degree but place zero in different spots. Absolute zero is 0 K and -273.15 \u00b0C, so shifting the origin by 273.15 aligns them. No multiplication is needed, which is why the conversion is an addition rather than a conversion ratio like every other unit on this page.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is 1 eV the same as 1 volt?<\/summary><div class=\"pf-faq-item-answer\">\nNo. The volt is a unit of electric potential difference and the electronvolt is a unit of energy. One electronvolt is the energy gained by a particle of charge e moving through a potential difference of 1 V, which equals exactly 1.602 176 634 x 10<sup>-19<\/sup> J. The numerical coincidence between the two values is why they are so often confused.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Should I use 273 or 273.15 when converting to kelvin?<\/summary><div class=\"pf-faq-item-answer\">\nUse 273.15 unless a question explicitly permits rounding. The offset 273.15 is exact by definition, so using 273 introduces an avoidable error of about 0.05 percent. In exam marking, the rounded value is usually tolerated at the final answer but not partway through a multi-step calculation.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is 1 bar the same as 1 atmosphere?<\/summary><div class=\"pf-faq-item-answer\">\nNo, though they are close. One bar is exactly 100 000 Pa, while one standard atmosphere is exactly 101 325 Pa, making 1 atm equal to 1.013 25 bar. The 1.3 percent difference is negligible for a rough estimate but will shift the answer to any gas-law or thermodynamics problem.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>How do you convert g\/cm^3 to kg\/m^3?<\/summary><div class=\"pf-faq-item-answer\">\nMultiply by 1000. The mass conversion divides by 1000 and the volume conversion multiplies by 10<sup>6<\/sup>, so the two combine to a net factor of 1000. Water, at 1.00 g\/cm<sup>3<\/sup>, is therefore 1000 kg\/m<sup>3<\/sup>. The common mistake is applying 10<sup>2<\/sup> rather than 10<sup>6<\/sup> to the cubed centimetre.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Which conversions are exact and which are rounded?<\/summary><div class=\"pf-faq-item-answer\">\nConversions defined by agreement are exact: 1 atm = 101 325 Pa, 1 bar = 100 000 Pa, 1 cal = 4.184 J, 1 lbf = 4.448 221 615 260 5 N, and since 2019, 1 eV = 1.602 176 634 x 10<sup>-19<\/sup> J. Anything derived from a measured quantity carries uncertainty instead. NIST marks exact factors in bold in its published tables.\n<\/div><\/details>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A practical reference for physics unit conversions, covering force, energy, pressure, temperature and SI prefixes with exact factors and worked examples.<\/p>\n","protected":false},"author":1,"featured_media":764,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-763","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\/763","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=763"}],"version-history":[{"count":7,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/763\/revisions"}],"predecessor-version":[{"id":1475,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/763\/revisions\/1475"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/764"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}