Model radiative heat loss using Stefan–Boltzmann physics accurately. Set emissivity, area, temperatures, and environment values. Get power, flux, and comparisons for real materials fast.
The Stefan–Boltzmann law for radiant power from a surface is: P = ε σ A T⁴
For net radiative exchange with an environment at Tenv: Pnet = ε σ A (T⁴ − Tenv⁴)
Tip: For accurate work, use kelvin and measured emissivity.
| Material | ε | Area (m²) | Surface (K) | Env (K) | Mode |
|---|---|---|---|---|---|
| Matte black paint | 0.95 | 1.0 | 500 | 300 | Net |
| Polished aluminum | 0.05 | 0.25 | 700 | 295 | Net |
| Ideal black surface | 1.00 | 0.10 | 900 | — | Emitted |
Radiation becomes a dominant heat-transfer path when convection is limited, when vacuum is present, or when surfaces run hot. The Stefan–Boltzmann relation links temperature to emitted power using a fourth-power law. That strong dependence means small temperature errors can create large power differences, especially above a few hundred kelvin.
The Stefan–Boltzmann constant is σ = 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴. In emitted mode, the calculator multiplies εσT⁴ to give radiant flux, then scales by area. This separation is useful because flux describes surface loading, while total power is needed for energy budgets and thermal sizing.
Ideal black surfaces have ε = 1, but engineered materials rarely do. Painted or oxidized surfaces often fall near 0.8–0.95, while polished metals can be 0.02–0.10. Changing ε from 0.1 to 0.9 increases radiated power ninefold at the same temperature, which is why finishes and coatings matter in thermal control.
For many designs, net exchange is more realistic than emitted power. Net mode uses εσA(T⁴ − Tenv⁴) to account for surrounding radiation. If the environment is warmer than the surface, net power becomes negative, indicating net gain. This sign information helps diagnose heating scenarios in furnaces, spacecraft, and enclosures.
Always compute in kelvin internally. The tool converts from Celsius or Fahrenheit and rejects non-physical inputs. As a quick check, 500 K is about 226.85 °C, while 300 K is about 26.85 °C. Conversions are especially important when comparing surfaces across test reports that mix temperature scales.
Consider ε = 0.95, A = 1 m², Ts = 500 K, and Tenv = 300 K. The net radiant flux is on the order of kilowatts per square meter, so radiative losses can rival heater power in laboratory setups. Doubling area doubles power, but raising temperature by 10% raises T⁴ by roughly 46%.
Emissivity uncertainty is often the largest contributor. Surface oxidation, roughness, and wavelength dependence can shift ε across operating conditions. Temperature measurement also matters: a 1% temperature error produces about a 4% error in T⁴, before emissivity and area tolerances are included.
Use emitted results for upper-bound power from a surface to deep space or a cold sink. Use net results for enclosures, ovens, and room-temperature surroundings. Combine this calculation with convection and conduction models to build a complete heat balance, then validate against measured steady-state temperatures.
Emitted power assumes the surface radiates to a very cold sink and ignores surroundings. Net power subtracts incoming environmental radiation using (T⁴ − Tenv⁴), showing whether the surface loses or gains energy overall.
The Stefan–Boltzmann law uses absolute temperature. Celsius and Fahrenheit are shifted scales, so using them directly would be incorrect. This calculator converts your input to kelvin before applying the fourth-power relation.
Use measured emissivity when possible. For estimates, matte paints and oxidized surfaces are often 0.8–0.95, while polished metals can be 0.02–0.10. Coatings can intentionally raise emissivity for better heat rejection.
Yes. Negative net power means the environment is effectively warmer in radiative terms, so the surface absorbs more radiation than it emits. This can happen in hot enclosures, near heaters, or under strong infrared sources.
No. This tool computes radiative exchange only. For total heat loss or gain, add convection (hAΔT) and conduction paths. Radiation is often dominant at high temperatures or in low-pressure conditions.
Very sensitive. Because power scales with T⁴, a small temperature increase produces a much larger power increase. Roughly, a 1% temperature change creates about a 4% change in radiative terms, before other uncertainties.
Almost never. σ is a physical constant for blackbody radiation. You might only change it for specialized unit systems or educational comparisons. For standard engineering work in SI units, keep the default value.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.