Planck Radiation Calculator Formula

Understand the math behind the planck radiation calculator. Each variable explained with a worked example.

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Formulas Used

Spectral Radiance

spectral_radiance = (2 * 6.626e-34 * pow(2.998e8, 2) / pow(wavelength, 5)) / (exp(6.626e-34 * 2.998e8 / (wavelength * 1.381e-23 * temperature)) - 1)

Variables

VariableDescriptionDefault
wavelengthWavelength(m)5e-7
temperatureTemperature(K)5778

How It Works

Planck's Law of Blackbody Radiation

Planck's law gives the spectral radiance of a blackbody as a function of wavelength and temperature.

Formula

B(lambda, T) = (2hc^2 / lambda^5) / (exp(hc / (lambda k_B T)) - 1)

  • *h* = 6.626 x 10^-34 J s
  • *c* = 2.998 x 10^8 m/s
  • *k_B* = 1.381 x 10^-23 J/K

    • This resolved the ultraviolet catastrophe and launched quantum mechanics.

    Worked Example

    Sun (5778 K) at 500 nm (green light).

    wavelength = 5e-7temperature = 5778
    1. 01Numerator: 2hc^2 / lambda^5
    2. 022 * 6.626e-34 * (2.998e8)^2 = 1.191e-16
    3. 03(5e-7)^5 = 3.125e-32
    4. 04Numerator = 1.191e-16 / 3.125e-32 = 3.811e15
    5. 05Exponent: hc/(lambda k T) = 6.626e-34 * 2.998e8 / (5e-7 * 1.381e-23 * 5778) = 4.97
    6. 06exp(4.97) - 1 = 143.6
    7. 07B = 3.811e15 / 143.6 = 2.654e13 W/m2/sr/m

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