{"id":724,"date":"2026-08-06T15:48:51","date_gmt":"2026-08-06T15:48:51","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=724"},"modified":"2026-08-06T15:48:53","modified_gmt":"2026-08-06T15:48:53","slug":"stefan-boltzmann-law","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/stefan-boltzmann-law\/","title":{"rendered":"What Is the Stefan-Boltzmann Law?"},"content":{"rendered":"\n
Definition<\/div>

\n\nThe Stefan-Boltzmann law states that the power radiated by a surface equals the Stefan-Boltzmann constant multiplied by its emissivity, its surface area, and its absolute temperature raised to the fourth power. Written P = \u03c3\u03b5AT4<\/sup>, it means that doubling an object’s absolute temperature multiplies the power it radiates by sixteen.\n\n<\/p><\/div>\n\n

Open an oven door at 220 \u00b0C and the heat hits your face before any hot air reaches you. That is thermal radiation arriving at the speed of light \u2014 and it does not scale gently.<\/p>\n\n

Push that oven to twice its absolute temperature and it would not glow twice as fiercely. It would pour out sixteen times<\/strong> the power. That single exponent is why a filament can light a room, why the Sun dominates our sky, and why Earth does not cook itself.<\/p>\n\n

What Is the Stefan-Boltzmann Law?<\/h2>\n\n

The Stefan-Boltzmann law says that the total power radiated by a surface across all wavelengths is proportional to the fourth power of its absolute temperature. Every object above absolute zero obeys it \u2014 you, this screen, an ice cube, a star.<\/p>\n\n

Josef Stefan found the relationship experimentally in 1879, working from measurements of hot platinum. Five years later Ludwig Boltzmann derived the same result from thermodynamics, treating radiation as a gas of photons exerting pressure. Experiment first, theory second \u2014 an unusually clean example of how physics actually advances.<\/p>\n\n

The law describes emission<\/em>, not the mechanism of transfer. If you want the wider picture of how radiation sits alongside conduction and convection as a mode of heat transfer<\/a>, that comparison is covered separately. Here we stay on the equation itself.<\/p>\n\n

Why “absolute” temperature is non-negotiable<\/h3>\n\n

T must be in kelvin. Always. A fourth power of a Celsius reading is physically meaningless, because Celsius has an arbitrary zero \u2014 and a negative Celsius temperature raised to the fourth power flips sign, which would imply an object absorbing energy simply for being cold.<\/p>\n\n

This is the single most common source of a wrong answer in exam scripts. Convert first: K = \u00b0C + 273.15. If you are shaky on why absolute scales exist at all, the distinction between heat and temperature<\/a> is the concept underneath it.<\/p>\n\n

The Stefan-Boltzmann Law Formula<\/h2>\n\n

The full form of the law, valid for any real surface, is:<\/p>\n\n

P = \u03c3\u03b5AT4<\/sup><\/div>\n\n

Every symbol, with its SI unit:<\/p>\n\n

\n\n\n\n\n\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\nNotes<\/th>\n<\/tr>\n<\/thead>\n
P<\/strong><\/td>\nRadiated power<\/td>\nwatt (W)<\/td>\nEnergy emitted per second<\/td>\n<\/tr>\n
\u03c3<\/strong><\/td>\nStefan-Boltzmann constant<\/td>\nW m-2<\/sup> K-4<\/sup><\/td>\n5.670374419 \u00d7 10-8<\/sup>, exact<\/td>\n<\/tr>\n
\u03b5<\/strong><\/td>\nEmissivity<\/td>\ndimensionless<\/td>\n0 to 1; equals 1 for a black body<\/td>\n<\/tr>\n
A<\/strong><\/td>\nRadiating surface area<\/td>\nm2<\/sup><\/td>\nThe area actually facing outward<\/td>\n<\/tr>\n
T<\/strong><\/td>\nAbsolute temperature<\/td>\nkelvin (K)<\/td>\nNever Celsius<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Note what P is: a rate. It is power measured in watts<\/a>, joules leaving every second, not a quantity of energy. A 500 W plate emits 500 joules each second for as long as you hold it at that temperature.<\/p>\n\n

Set \u03b5 = 1 and you get the idealised black-body form, P = \u03c3AT4<\/sup>. If you would rather not push the fourth powers through a calculator by hand, our Stefan-Boltzmann Calculator<\/a> takes \u03b5, A and T and returns the radiated power \u2014 and rearranges to solve for temperature when you already know the power.<\/p>\n\n

The constant is now exact<\/h3>\n\n

Since the 2019 SI redefinition, \u03c3 is no longer a measured quantity with an experimental uncertainty. It is fixed by definition, because it is built from the Planck constant, the Boltzmann constant and the speed of light \u2014 all of which now have exact defined values.<\/p>\n\n

That is why you will see it quoted to ten significant figures: \u03c3 = 5.670374419 \u00d7 10-8<\/sup> W m-2<\/sup> K-4<\/sup>. For any exam or engineering estimate, 5.67 \u00d7 10-8<\/sup> is plenty.<\/p>\n\n

<\/span>Stefan-Boltzmann Law Lab<\/span><\/div>