How this calculator works
Planck law gives radiance per unit spectral interval. Frequency, wavelength and reciprocal-wavelength bins have different widths, so their peak locations are not obtained by simply converting one peak into another. Photon spectra divide energy radiance by the energy of one photon. A greybody multiplies every spectral value by constant emissivity. The integrated exitance is π times radiance for this Lambertian emitter. Temperature inversion assumes known emissivity and the selected spectral units. Physical constants retain their SI definitions.
Formula
Bλ = ε 2hc²/[λ⁵(exp(hc/λkT)-1)] per metre of wavelength; divide by 10^9 for per nm. Bν = ε 2hν³/[c²(exp(hν/kT)-1)]. Bσ = ε 2hc²σ³/[exp(hcσ/kT)-1]. Photon radiance is B divided by photon energy. Energy exitance = εσSB T⁴.
Worked example
At 300 K and emissivity 1, integrated energy exitance is about 459.3003 W/m2 and the wavelength-energy peak is 9659.24 nm. An emissivity of 0.5 halves radiance and exitance without moving the peak.
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Frequently asked questions
Why do frequency and wavelength peaks differ?
A spectrum is a density per coordinate interval. The reciprocal transformation changes bin widths and therefore changes the density maximum.
What is photon space?
It counts emitted photons per second instead of weighting each photon by its energy.
Which wavenumber is used?
The coordinate is 1/λ in reciprocal metres. It does not include the 2π factor of angular wavenumber.