#1 Free Blackbody Radiation Calculator 2025

How to Use This Calculator

This calculator determines key properties of blackbody radiation based on its temperature.

• Enter the temperature (T) of the blackbody in Kelvin (K).
• Optionally, to calculate spectral radiance at a specific point, enter the wavelength (λ) and select its units (nm, µm). If left blank, only peak wavelength and total power will be calculated.
• Click the "Calculate Blackbody Radiation" button.
• Results, including peak wavelength, total radiated power, spectral radiance (if applicable), and a step-by-step solution, will be displayed below.

Theory: Blackbody Radiation

A blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. When in thermal equilibrium, it emits electromagnetic radiation called blackbody radiation. The characteristics of this radiation depend only on the body's temperature.

Key concepts and laws governing blackbody radiation include:

• Planck's Law: Describes the spectral radiance (power per unit area, per unit solid angle, per unit wavelength) emitted by a blackbody at a given temperature and wavelength. This law was a pioneering result of quantum mechanics.
• Wien's Displacement Law: States that the wavelength at which the spectral radiance of blackbody radiation is at its maximum (λ_peak) is inversely proportional to the absolute temperature of the blackbody. Hotter objects emit light at shorter (bluer) peak wavelengths.
• Stefan-Boltzmann Law: States that the total power radiated per unit surface area of a blackbody (across all wavelengths) is directly proportional to the fourth power of the blackbody's absolute temperature.

These laws are fundamental in astrophysics (for understanding stars), thermodynamics, and lighting design.

Formulas Used

• 1. Wien's Displacement Law (λ_peak):

  λpeak = b / T

  • b (Wien's constant) ≈ 2.897771955 × 10^-3 m·K
  • T = Absolute temperature in Kelvin (K)
• 2. Stefan-Boltzmann Law (P_total/Area):

  P/A = σ × T4

  • σ (Stefan-Boltzmann constant) ≈ 5.670374 × 10^-8 W·m^-2·K^-4
• 3. Planck's Law (B_λ(T)): Spectral Radiance

  Bλ(T) = (2hc2 / λ5) × [1 / (e(hc / λkBT) - 1)]

  • h (Planck's constant) ≈ 6.62607 × 10^-34 J·s
  • c (Speed of light) ≈ 2.99792 × 10⁸ m/s
  • kB (Boltzmann constant) ≈ 1.38065 × 10^-23 J/K
  • λ = Wavelength in meters (m)
  • Units of B_λ(T): W·sr^-1·m^-3 (or W·sr^-1·m^-2·m^-1)

Calculate Blackbody Radiation

Calculation Results