Stefan-Boltzmann Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The power radiated by a body is calculated with P = σ × ε × A × T⁴ (temperature in kelvins). A perfect black body of 1 m² at 20°C (293.15 K) radiates about 418.74 W.
Explanation
The Stefan-Boltzmann law describes the total power radiated as heat by a body at any temperature above absolute zero: every object, even at room temperature, continuously emits thermal electromagnetic radiation, usually in the infrared and therefore invisible to the naked eye. This power depends on the absolute temperature raised to the fourth power — an extremely strong dependence, which explains why doubling a body's absolute temperature multiplies the power it radiates by 16 (2⁴). Emissivity (ε) expresses how efficiently a material radiates compared to a theoretical perfect black body (ε = 1, an idealized object that absorbs and re-emits all radiation): a polished metal surface has very low emissivity (around 0.03 to 0.1), while a matte or organic surface, like human skin, comes much closer (about 0.95 to 0.98). This law is central to many fields: it explains a significant share of the heat losses of a building or a body to its environment, it allows the surface temperature of stars to be estimated from their observed radiation, and it underlies the design of thermal cameras and radiative cooling systems.
Example: perfect black body, 1 m², 20°C
Inputs
Emissivity: 1 (perfect black body). Surface: 1 m². Temperature: 20°C (293.15 K).
Calculation
P = 5.670 × 10⁻⁸ × 1 × 1 × 293.15⁴ ≈ 418.74 W.
Result
This body radiates about 418.74 W as heat.
Frequently asked questions
Why does radiated power depend on temperature to the fourth power?
This T⁴ dependence is a result from statistical physics and electromagnetism (derived from Planck's law of black-body radiation, integrated over all wavelengths). In practice, it means a small increase in absolute temperature produces a disproportionate rise in radiated power: doubling the absolute temperature multiplies the radiated power by 16.
What is a perfect black body, and why doesn't it really exist?
A perfect black body is an idealized object that fully absorbs all electromagnetic radiation it receives, without reflecting or transmitting any of it, and then re-emits that radiation with perfect efficiency (emissivity ε = 1). No real material achieves exactly this perfect efficiency, but some come very close (such as soot or certain specially designed laboratory materials), which makes it a very useful theoretical model for calculations, later adjusted by the real emissivity of the material studied.
Does this calculation account for radiation received from the surroundings?
No, this calculator only gives the power emitted by the body itself. In a real environment, the object also receives thermal radiation from its surroundings (walls, ambient air, other objects): the net power actually lost or gained results from the difference between what the body emits and what it absorbs, a more complex balance not covered by this simplified calculation.