Enter a surface's area, temperature, and emissivity to calculate the radiated thermal power using the Stefan-Boltzmann Law (P = εσAT⁴). Choose a preset material or enter a custom emissivity value — the calculator returns radiated power in watts along with the equivalent power density per square metre. Also try the find Result with Newton's Law of Cooling Calculator.
Radiated Power (P)
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Power Density (P/A)
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Temperature in Kelvin
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σ × T⁴
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The Stefan-Boltzmann Law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature (T⁴). For real surfaces, the radiated power is scaled by the emissivity (ε), giving the formula P = εσAT⁴, where σ is the Stefan-Boltzmann constant (5.670367 × 10⁻⁸ W/m²·K⁴). See also our Combined Gas Law Calculator.
Emissivity (ε) is a dimensionless number between 0 and 1 that describes how efficiently a surface radiates energy compared to an ideal black body (ε = 1). A polished metal like aluminium foil has very low emissivity (~0.09), meaning it radiates very little heat, while asphalt or human skin have high emissivity (~0.88–0.95) and radiate close to the theoretical maximum.
The law assumes the surface radiates uniformly in all directions (isotropic radiation), the emissivity is constant across all wavelengths (grey body assumption), and the surrounding environment is at absolute zero. In real-world scenarios, net radiation also accounts for the temperature of the surroundings, but this calculator computes total emitted power only.
The calculator uses SI units internally: area in square metres (m²), temperature in kelvin (K), and power in watts (W). You can enter temperature in Celsius or Fahrenheit — the tool converts automatically to kelvin before applying the formula. You might also find our calculate Clausius-Clapeyron Equation Final Vapor Pressure (P₂) useful.
Because power scales with T⁴ (the fourth power of absolute temperature), even small increases in temperature cause a dramatic rise in radiated power. For example, doubling the absolute temperature increases the radiated power by a factor of 2⁴ = 16. This non-linear relationship makes high-temperature objects radiate enormously more energy than cool ones.
Yes. By setting emissivity to a value less than 1, the calculator handles real (grey body) surfaces. You can choose from the preset material list — which includes aluminium foil, brick, glass, and more — or enter any custom emissivity value between 0 and 1 for your specific material.
The Stefan-Boltzmann constant (σ) is a fundamental physical constant equal to 5.670367 × 10⁻⁸ W·m⁻²·K⁻⁴. It relates the temperature of a black body to the intensity of radiation it emits and appears in all thermal radiation calculations.
The law applies strictly to opaque, grey-body surfaces with constant emissivity across wavelengths. It does not account for convection or conduction heat transfer, nor does it model wavelength-dependent emission (for that, Planck's law is required). It also assumes the radiating surface is at a uniform temperature throughout.