Blackbody Radiation Calculator

A blackbody is an idealised object that absorbs all incoming electromagnetic radiation and re-emits it purely based on its temperature. The spectrum it emits — described by Planck's law — was the key observation that led to the development of quantum mechanics. Real objects approximate blackbody behaviour with an emissivity factor between 0 and 1.

Planck's law gives the spectral radiance B(λ,T) = (2hc²/λ⁵) × 1/(e^(hc/λk_BT) − 1), where h is Planck's constant (6.626×10⁻³⁴ J·s), c is the speed of light, k_B is Boltzmann's constant (1.381×10⁻²³ J/K), λ is wavelength, and T is temperature in Kelvin. This formula quantises radiation and predicts the observed spectrum perfectly.

932 °F equals 500 °C, or 773.15 K. Using Wien's displacement law (λ_peak = 2.898×10⁶ nm·K / T), the peak wavelength is approximately 3749 nm, which falls in the mid-infrared region — invisible to the human eye.

The total power radiated per unit area is given by the Stefan-Boltzmann law: P = ε × σ × T⁴, where σ = 5.67×10⁻⁸ W·m⁻²·K⁻⁴ is the Stefan-Boltzmann constant, ε is the emissivity, and T is temperature in Kelvin. A perfect blackbody (ε = 1) at 5778 K radiates about 63.2 MW/m².

Wien's displacement law states that the peak wavelength of blackbody emission is inversely proportional to temperature: λ_peak = b/T, where b ≈ 2.898×10⁶ nm·K. As temperature increases, the peak wavelength shifts to shorter (bluer) wavelengths, explaining why hotter stars appear blue and cooler stars appear red.

As temperature rises, two things happen: the peak of the emission curve shifts to shorter wavelengths (Wien's law), and the total emitted power increases dramatically (proportional to T⁴). A body at room temperature (~300 K) emits mostly in the far infrared around 9700 nm, while the Sun at 5778 K peaks in the visible green region at ~500 nm.

Emissivity (ε) is a dimensionless factor from 0 to 1 that describes how efficiently a real surface emits thermal radiation compared to a perfect blackbody. A value of 1 means perfect blackbody emission. Real materials have emissivities less than 1 — for example, polished metals can be as low as 0.05, while human skin is about 0.98. The spectral radiance is simply multiplied by ε.

In a quantum mechanical sense, yes — black holes emit Hawking radiation with a near-perfect blackbody spectrum. However, the temperature of a stellar-mass black hole's Hawking radiation is extraordinarily low (nanokelvins), making it completely undetectable in practice. The concept is important theoretically because it links thermodynamics, quantum mechanics, and general relativity.