Blackbody Radiation Calculator

A blackbody is an idealized physical object that absorbs all incident electromagnetic radiation regardless of frequency or angle of incidence. Despite the name, a perfect blackbody at thermal equilibrium emits a characteristic spectrum of radiation determined solely by its temperature — this is blackbody radiation. The spectrum spans from radio waves through visible light to gamma rays, with the peak wavelength shifting to shorter values as temperature increases.

No real object is a perfect blackbody, but many approximate one well enough for the physics to be extremely useful. Stars (including our Sun) radiate approximately as blackbodies — the Sun's surface temperature of 5,778 K produces a spectrum peaking in the visible range at about 500 nm (green-yellow), which is precisely why our eyes evolved sensitivity in this wavelength range. The cosmic microwave background is the most perfect blackbody ever observed, at T = 2.725 K.

Blackbody radiation is described by three interconnected laws:

Before Planck, classical physics predicted that a blackbody would emit infinite power at short wavelengths — the notorious ultraviolet catastrophe. The Rayleigh-Jeans law (derived from classical equipartition) gave B(λ,T) ∝ T/λ⁴, which blows up as λ → 0. Planck solved this in 1900 by introducing the radical idea that electromagnetic energy is quantized in discrete packets E = hν. His formula matched experimental data perfectly and launched quantum mechanics.

This calculator computes the spectral radiance at any arbitrary wavelength using Planck's full formula. For wavelengths much longer than the peak (λ >> λ_max), the Rayleigh-Jeans approximation is accurate. For wavelengths much shorter than the peak, the Wien approximation holds. Planck's genius was to interpolate between these two regimes with a single formula that reduced to each limit in the appropriate range.

Blackbody radiation is fundamental to astronomy and astrophysics. A star's color directly indicates its surface temperature — blue stars are hot (T > 10,000 K), yellow stars like the Sun are intermediate (~5,700 K), and red stars are cool (< 3,500 K). By fitting a star's spectrum to a blackbody curve, astronomers determine its effective temperature, and from the Stefan-Boltzmann law combined with the star's luminosity, they derive its radius. This technique has classified millions of stars.

In climate science, Earth's energy balance is a blackbody problem. The Sun heats Earth to about 255 K (radiative equilibrium temperature without atmosphere), but the greenhouse effect raises the surface to ~288 K. The difference — 33 K of greenhouse warming — is calculated using modified blackbody models with atmospheric absorption bands. Earth radiates primarily in the infrared (peak ~10 μm), which CO₂ molecules absorb strongly, creating the greenhouse effect that makes our planet habitable.