Radiação (Stefan-Boltzmann)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Stefan-Boltzmann
About this calculator
The thermal radiation calculator based on the Stefan-Boltzmann law allows you to compute the power radiated by a blackbody or real body (considering emissivity). The formula P = εσAT⁴ relates radiated power (P) to emissivity (ε, between 0 and 1), the Stefan-Boltzmann constant (σ ≈ 5.67×10⁻⁸ W/m²K⁴), surface area (A), and absolute temperature (T in Kelvin). This tool is essential for understanding heat transfer by radiation, common in furnaces, stars, infrared sensors, and thermal insulation.
To use the calculator, enter temperature (in °C or K), area (m²), and emissivity (0 to 1). The result is radiated power in watts. Remember to convert °C to K (T(K) = T(°C) + 273.15). Emissivity depends on material: dark bodies have ε near 1 (e.g., soot), while polished surfaces have low ε (e.g., polished aluminum ε≈0.04). The calculator assumes an opaque, isotropic body without external reflections.
Use cases include sizing heat sinks, estimating thermal loss through windows, calculating filament temperature in lamps, and analyzing solar collector efficiency. Radiation is the only heat transfer mode in vacuum, crucial for space applications. Beware of units: always use Kelvin for temperature, as the law requires absolute scale. Common mistakes include forgetting to convert °C or using incorrect emissivity for the material.
Frequently asked questions
Do I need to convert temperature to Kelvin?
Yes, the Stefan-Boltzmann law requires absolute temperature in Kelvin. If you enter in °C, the calculator converts automatically.
What is emissivity and how do I choose the value?
Emissivity is a material's efficiency in radiating heat, ranging from 0 (perfect reflector) to 1 (blackbody). Consult tables for common materials; for most non-metallic solids, ε≈0.9.
Does the calculator consider incident radiation from the surroundings?
No, it only calculates the power radiated by the body. For net balance, subtract absorbed radiation from the environment (P_net = εσA(T⁴ - T_surr⁴)).
Can I use it to calculate filament temperature?
Yes, if you know power and area. For example, a 100 W lamp with a 0.5 cm² filament and ε≈0.3 reaches about 2500 K. Remember that some power is lost through conduction and convection.
What is the difference between radiation and convection?
Radiation does not require a medium (propagates in vacuum), while convection depends on fluid. At high temperatures, radiation dominates; at low temperatures, convection is more relevant.