Blackbody Radiation Calculator

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Use this blackbody radiation calculator to find spectral radiance at a chosen wavelength or frequency, plus the correct peak for that same mode, the Wien peak wavelength, and total emitted power from temperature.

Advanced options
Units and inputs
Surface and material
Spectral output
Temperature (Kelvin) (K)
This is the temperature used in all calculations.
Spectral radiance at chosen wavelength/frequency
B_lambda is per meter of wavelength. B_nu is per Hz of frequency. They are not directly comparable without converting variables.
Peak wavelength/frequency for this mode
The peak is different depending on whether you plot per wavelength or per frequency.
Wien peak wavelength (from displacement law) (nm)
This corresponds to the peak of the per-wavelength spectrum (B_lambda).
Total radiated power per area (Stefan-Boltzmann) (W/m^2)
This is integrated over all wavelengths and over the hemisphere above the surface.
Total radiated power from area (W)
If area is blank, this shows N/A.
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How to use our Blackbody Radiation Calculator

  1. Choose a Calculation mode: Per wavelength (B_lambda) uses wavelength, and Per frequency (B_nu) uses frequency.
  2. Enter the temperature and (in Advanced options) pick the temperature unit you are typing (K, C, or F).
  3. If you chose Per wavelength, enter the wavelength and (in Advanced options) choose the wavelength unit.
  4. If you chose Per frequency, enter the frequency in THz (in Advanced options).
  5. Optional: enter emissivity (0 to 1) if the surface is not a perfect blackbody (1.0).
  6. Optional: enter emitting surface area (m^2) to get total power in watts.
  7. Optional: choose Spectral output style to see radiance (B) or hemispherical exitance (M = pi times B).
  8. Click Calculate.
  9. Read the outputs: the calculator shows spectral value at your chosen point, the peak for the selected mode, the Wien peak wavelength, and total power per area (and from area if provided).

Definitions

Blackbody: An ideal object that absorbs and emits radiation as well as possible; it is defined by its temperature.

Temperature (Kelvin): The temperature scale used in the formulas; it starts at absolute zero (0 K).

Wavelength: The distance between wave peaks of light; shorter wavelength means higher energy per photon.

Frequency: How many wave cycles happen each second, measured in hertz (Hz).

Spectral radiance (B): Power coming from a surface in a particular direction, per unit area, per unit wavelength (B_lambda) or per unit frequency (B_nu), per steradian (sr).

Spectral exitance (M): Power leaving a surface into the whole hemisphere above it, per unit area, per unit wavelength/frequency; for a Lambertian emitter, M = pi times B.

Wien peak wavelength: The wavelength where the per-wavelength spectrum (B_lambda) is highest; it uses Wien constant b [2].

Stefan-Boltzmann law: Total power per area from a blackbody is sigma times T to the 4th power; sigma is the Stefan-Boltzmann constant [1].

Emissivity: A number from 0 to 1 that scales how strongly a real surface emits compared to a perfect blackbody (1).

Methodology

Inputs and unit conversions

Temperature is converted to Kelvin (K) before any physics math. If you select C: K = C + 273.15. If you select F: K = (F - 32) * 5/9 + 273.15. The calculator requires K > 0.

In Per wavelength (B_lambda) mode, wavelength is converted to meters (m) and must be > 0.

In Per frequency (B_nu) mode, frequency is converted from THz to Hz (1 THz = 1e12 Hz) and must be > 0.

Planck spectral radiance

The calculator uses the form that matches your mode. This matters because the peak location is different for B_lambda vs B_nu.

B_lambda(lambda,T) = (2*h*c^2)/(lambda^5) * 1/(exp(h*c/(lambda*kB*T)) - 1)

B_nu(nu,T) = (2*h*nu^3)/(c^2) * 1/(exp(h*nu/(kB*T)) - 1)

If emissivity is provided, the reported spectral value is multiplied by emissivity. Emissivity must be from 0 to 1.

Numerical stability for exp()

Let x be the exponent term (for example x = h*c/(lambda*kB*T) in B_lambda). To avoid overflow and rounding issues, the calculator evaluates exp(x) - 1 using a safe helper: if x is very large (about > 700), it uses exp(x) in a way that avoids Infinity in the final division; if x is very small (about |x| < 1e-5), it uses exp(x) - 1 approximately equal to x.

Spectral exitance option (hemisphere over the surface)

If you choose Exitance, the calculator converts from radiance to hemispherical exitance using the Lambertian relation.

M_lambda = pi * B_lambda

M_nu = pi * B_nu

Peak location outputs

The calculator reports a peak for the selected mode (peak of B_lambda in wavelength mode, peak of B_nu in frequency mode). It also reports the common Wien peak wavelength from the displacement law, which is specifically for the peak of B_lambda.

lambda_peak_wien = b / T

Wien displacement constant b is taken from NIST [2].

Total emitted power (all wavelengths)

Total radiated power per area is computed with the Stefan-Boltzmann law and includes emissivity if provided.

M_total = emissivity * sigma * T^4

Stefan-Boltzmann constant sigma is taken from NIST [1].

Total power from a surface area

If you enter surface area A (m^2), the calculator multiplies total exitance by area. If area is blank, this output is shown as N/A. If area is provided, it must be > 0.

P_total = M_total * A

Sources

  1. CODATA Value: Stefan-Boltzmann constant - NIST
  2. CODATA Value: Wien wavelength displacement law constant &dagger - NIST