PhysicsCalcs
Thermodynamics

Blackbody Radiation Calculator

Calculate peak wavelength, total radiated power, stellar luminosity, spectral radiance, and photon energy for any blackbody temperature.

Interactive calculator

Blackbody Radiation Calculator

Calculate peak wavelength (Wien), total power (Stefan-Boltzmann), stellar luminosity, spectral radiance (Planck), and photon energy.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose Wien, Stefan-Boltzmann, Planck, luminosity, or stellar temp mode.
  • Enter temperature in Kelvin (and radius/area if needed).
  • Get peak wavelength, power, and spectral data.

Table of Contents

Key Takeaways

  • Wien’s law: λₘₐₓ = b/T — hotter objects peak at shorter wavelengths.
  • Stefan–Boltzmann: P = σT⁴A — radiated power grows as the 4th power of temperature.
  • Planck’s law gives the full spectral distribution of thermal radiation.
  • The Sun (~5778 K) peaks at ~502 nm (green-yellow).
  • The cosmic microwave background (2.725 K) peaks at ~1.06 mm (microwave).
  • Doubling temperature increases total power by 16×.

What Is Blackbody Radiation?

A blackbody is an idealized object that absorbs and emits all frequencies of electromagnetic radiation. The spectrum it emits depends only on its temperature, following Planck’s law. Stars, planets, and even the cosmic microwave background closely approximate blackbody emitters.

Wien’s Displacement Law

λmax=bT\lambda_{max} = \frac{b}{T}

Wien’s law relates the peak emission wavelength to temperature. As temperature increases, the peak shifts to shorter (bluer) wavelengths. The displacement constant b = 2.898 × 10⁻³ m·K.

Stefan–Boltzmann Law

P=σT4AP = \sigma T^4 A

Total radiated power scales as T⁴. Doubling temperature increases radiation by 16×. The Stefan–Boltzmann constant σ = 5.670 × 10⁻⁸ W/(m²·K⁴).

Planck’s Law

B(λ,T)=2hc2λ5(ehc/λkBT−1)B(\lambda,T) = \frac{2hc^2}{\lambda^5\left(e^{hc/\lambda k_B T} - 1\right)}

Planck’s law gives the spectral radiance at every wavelength. It resolved the ultraviolet catastrophe and launched quantum physics.

Stellar Luminosity

L=4πR2σT4L = 4\pi R^2 \sigma T^4

Combining the Stefan–Boltzmann law with a sphere’s surface area gives the total luminosity of a star. The Sun’s luminosity is L☉ = 3.828 × 10²⁶ W.

How to Use

  1. Select a mode matching your question (Wien, Stefan-Boltzmann, Planck, luminosity, stellar temp).
  2. Enter temperature and other parameters.
  3. Click Calculate for full results.

Examples

Sun (5778 K)

λmax = 2.898e-3 / 5778 ≈ 501 nm (green)

CMB (2.725 K)

λmax = 2.898e-3 / 2.725 ≈ 1.06 mm (microwave)

Sun’s luminosity

L = 4π × (6.957e8)² × 5.67e-8 × 5778&sup4; ≈ 3.85 × 10²&sup6; W

FAQ

What is a blackbody?›

An ideal blackbody is a perfect absorber and emitter of radiation at all wavelengths. Its emission spectrum depends only on temperature. Stars, planets, and the cosmic microwave background approximate blackbody behaviour.

What is Wien’s displacement law?›

Wien’s law states that the peak emission wavelength is inversely proportional to temperature: λₘₐₓ = b/T, where b = 2.898 × 10⁻³ m·K.

What is the Stefan–Boltzmann law?›

It gives the total power radiated per unit area: j = σT⁴, where σ = 5.670 × 10⁻⁸ W/(m²·K⁴). Total power P = σT⁴ × surface area.

Why does the Sun look white-yellow?›

The Sun’s peak wavelength (~502 nm) is in the green, but it emits broadly across the visible spectrum. Our eyes perceive the mix as white/yellow.

What is spectral radiance?›

Spectral radiance B(λ,T) from the Planck function gives the power emitted per unit area, per steradian, per unit wavelength at a specific wavelength and temperature.

How does emissivity affect real objects?›

Real objects emit less than a perfect blackbody. Their emission is P = εσT⁴A, where emissivity ε ranges from 0 to 1. This calculator assumes ε = 1 (ideal blackbody).

Sources

  1. OpenStax – Blackbody Radiation
  2. HyperPhysics – Planck Radiation
  3. NIST – Fundamental Constants
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish