Blackbody Radiation Calculator
Every Object Glows — Just Not Always Visibly
Any object above absolute zero radiates electromagnetic energy from its surface, and the hotter it gets, the more intensely it radiates. This is why a stovetop element goes from invisible heat to dull red to bright orange as its temperature climbs. The Stefan-Boltzmann law quantifies exactly how much power an idealized "blackbody" emits per unit area at a given temperature, and this calculator applies it directly.
The Formula
P/A is the radiant power emitted per square meter (W/m²), T is absolute temperature in kelvin, and σ is the Stefan-Boltzmann constant, 5.67×10&supminus;&sup8; W/(m²·K&sup4;). Because temperature is raised to the fourth power, radiated power grows extremely fast with even modest temperature increases.
Why the Fourth Power Matters
- Astrophysics — a star's luminosity is derived largely from its surface temperature and radius using this exact relationship.
- Thermal engineering — radiative heat loss from furnaces, engines, and electronics enclosures is calculated with the Stefan-Boltzmann law once emissivity is factored in.
- Climate science — Earth's radiative balance with the Sun and space is modeled using blackbody radiation principles.
- Incandescent lighting — a filament's light output and efficiency are tied directly to how hot it can be run before failing.
How Radiated Intensity Scales With Temperature
| Object | Temperature | Radiant Intensity |
|---|---|---|
| Cosmic microwave background | 2.725 K | 3.126×10&supminus;&sup6; W/m² |
| Room-temperature surface | 300 K | 459.27 W/m² |
| Incandescent filament | 3,000 K | 4.593×10&sup6; W/m² |
| Sun's surface | 5,778 K | 6.320×10&sup7; W/m² |
Going from 300 K to 3,000 K — a 10× increase in temperature — increases radiant intensity by a factor of 10,000, exactly as predicted by the fourth-power relationship.
How to Use This Calculator
- Enter the object's Temperature and choose the unit, Kelvin or Celsius.
- Optionally enter a Surface Area in m² to also get total radiated power, not just intensity.
- Select Calculate to see radiant intensity in W/m², and total power in watts if an area was provided.
Related Calculations
For the energy carried by individual light particles rather than total radiated power, see the Photon Energy Calculator, or convert between a light source's wavelength and frequency with the Wavelength Calculator.