Calculate thermal radiation power, temperature, or emissivity using the Stefan-Boltzmann law for blackbody and real surface radiation analysis.
The Stefan-Boltzmann law describes how the total energy radiated per unit surface area of a body is proportional to the fourth power of its absolute temperature. This fundamental relationship governs thermal radiation from stars, furnaces, electronic components, building surfaces, and the human body. The Stefan-Boltzmann Calculator helps engineers, physicists, and students compute radiated power, effective temperature, or required emissivity for any thermal radiation scenario.
The law is expressed as P = εσAT⁴, where ε is emissivity (0 to 1), σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴), A is surface area, and T is absolute temperature in Kelvin. Perfect blackbodies have ε = 1, while real surfaces range from 0.02 (polished silver) to 0.98 (lampblack). The T⁴ dependence means that doubling temperature increases radiative power 16-fold.
This calculator handles net radiation exchange between a surface and its surroundings, critical for HVAC design, electronic cooling, industrial furnace design, and astrophysics. Enter any combination of known values to solve for the unknown parameter.
Use this calculator when you need a first-pass radiation estimate for a hot surface, enclosure, or blackbody-style problem without doing the T-to-the-fourth arithmetic by hand. It is useful for thermal design, heat-loss comparisons, and sanity-checking whether radiation is a minor term or a dominant one. That is often enough to decide whether you need to model radiation explicitly or can treat it as a small correction.
Stefan-Boltzmann Law: P = ε × σ × A × T⁴. Net radiation: P_net = ε × σ × A × (T_surface⁴ - T_surroundings⁴). Wien's displacement: λ_max = 2897.8 / T (μm). Stefan-Boltzmann constant σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴).
Result: About 34.4 kW total radiated power
A surface at 500°C (773.15 K) with emissivity 0.85 and 2 m² area radiates about 34.4 kW in total. When the surroundings are at 25°C, the net radiation drops slightly to about 33.6 kW. The peak emission wavelength is around 3.75 μm in the mid-infrared.
A perfect blackbody absorbs all incident radiation and emits the maximum possible thermal radiation at every wavelength. The Stefan-Boltzmann law gives the total integrated power across all wavelengths. The spectral distribution follows Planck's law, with the peak shifting to shorter wavelengths as temperature increases (Wien's law).
Real surfaces emit less than a blackbody at the same temperature, quantified by emissivity. Some materials have emissivity that varies with wavelength (selective emitters), which is exploited in solar absorber coatings that absorb visible light efficiently while minimizing infrared re-radiation.
In electronics thermal management, radiation often contributes 20-40% of total heat dissipation from enclosures and heat sinks. Anodized or painted surfaces with ε = 0.85-0.95 radiate much more effectively than bare aluminum (ε = 0.05-0.1). This simple surface treatment can reduce component temperatures by 10-20°C.
In building energy modeling, long-wave infrared radiation exchange between building surfaces, sky, and ground significantly affects heating and cooling loads. Cool roof coatings with high solar reflectance and high thermal emissivity can reduce cooling energy by 10-30% in hot climates.
The Stefan-Boltzmann law is the primary tool for determining stellar luminosities and effective temperatures. Combined with observed luminosity and distance, it yields stellar radii. It also governs planetary energy budgets — Earth's equilibrium temperature is determined by the balance between absorbed solar radiation and emitted infrared radiation, the foundation of climate science.
σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴). It relates the total energy radiated by a blackbody to the fourth power of its temperature. It's derived from fundamental constants: σ = 2π⁵k⁴/(15h³c²).
Emissivity (ε) ranges from 0 to 1 and describes how efficiently a surface emits thermal radiation compared to a perfect blackbody. Polished metals have low emissivity (0.02-0.1), while most non-metals have high emissivity (0.8-0.98).
The T⁴ relationship arises from integrating Planck's spectral radiation law over all wavelengths. This strong dependence means a small temperature increase significantly boosts radiation. Doubling temperature from 300K to 600K increases radiation 16-fold.
Wien's law gives the wavelength of peak emission: λ_max = 2897.8 / T (in μm when T is in Kelvin). At room temperature (300K), peak emission is at 9.7 μm (far-infrared). The Sun (5778K) peaks at 0.50 μm (visible green).
The human body at 37°C (310K) with emissivity ~0.98 and ~1.7 m² surface area radiates about 800 W. But absorption from surroundings at ~22°C returns ~640 W, so the net radiative heat loss is about 160 W.
Radiation dominates at high temperatures (>500°C), in vacuum environments (no convection), and for surfaces with large temperature differences to surroundings. In space, radiation is the ONLY heat transfer mechanism.