Blackbody Radiation
Planck's law spectral radiance curve, Wien's displacement law, Stefan-Boltzmann radiant exitance and the share of power in a wavelength band.
Peak wavelength (Wien)
501.5 nm
λ_peak T = 2897.8 µm·K
Peak spectral radiance
2.638e+4 W/(m²·sr·nm)
Radiant exitance M = σT⁴
6.320e+7 W/m²
Power per unit area into the hemisphere
Radiance L = σT⁴/π
2.012e+7 W/(m²·sr)
Same in every direction (Lambertian)
Fraction in 380–780 nm
46.53 %
2.940e+7 W/m² in the band
Spectral radiance vs wavelength
- 5778 K
- Band 380–780 nm
L_λ = 2hc² / (λ⁵ (e^(hc/λk_BT) − 1)), M_λ = π L_λ
λ_peak = b / T, b = 2.897772 × 10⁶ nm·K
M = σT⁴, σ = 5.670374 × 10⁻⁸ W m⁻² K⁻⁴
These are the values for an ideal blackbody in vacuum; a real surface emits ε(λ) times as much. The peak of the spectrum per unit frequency or per wavenumber lies at a longer wavelength than λ_peak (about 1.76 λ_peak), because the curve's shape depends on the spectral variable. The band fraction uses the series form of the blackbody function (Siegel & Howell).
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Exact Planck, Wien and Stefan–Boltzmann laws for an ideal blackbody (emissivity 1) radiating into vacuum, with CODATA constants; radiance is M/π. Real surfaces emit ε(λ) times these values.
- Howell J. R., Mengüç M. P., Daun K., Siegel R. (2020). Thermal Radiation Heat Transfer, 7th ed. CRC Press. Blackbody functions and band fractions. doi:10.1201/9780429327308
- Mohr P. J., Newell D. B., Taylor B. N., Tiesinga E. (2025). CODATA recommended values of the fundamental physical constants: 2022. Rev. Mod. Phys. 97, 025002. doi:10.1103/RevModPhys.97.025002
Report a problem
Related calculators