Black-body radiation (Planck + Wien + Stefan–Boltzmann)

Calculate and chart the black-body radiation curve, compare temperatures, analyze UV/visible/IR bands, export CSV, and generate a printable report.

Black-body radiation (Planck + Wien + Stefan–Boltzmann)

Explore the spectral curve of a black body, compare temperatures, and compute UV/visible/IR power with CSV export and a printable report.

Main input

Main input

Remember: Mλ = π·Bλ.
Advanced options
Results

Results

λmax —
M total —
Peak band —

The visible band (380–700 nm) is highlighted and the Wien peak is marked with a vertical line.

Values at selected wavelengths

λ Value % of maximum Actions
What is a black body?

It is an ideal emitter that absorbs all incident radiation and emits energy solely as a function of its temperature.

What is the difference between Planck, Wien, and Stefan–Boltzmann?

Planck describes the full spectral distribution, Wien gives the wavelength of the maximum, and Stefan–Boltzmann relates total power to T⁴.

Why does the peak change with temperature?

As temperature increases, the distribution shifts to shorter wavelengths (Wien's displacement law).

What do the UV, visible, and IR bands mean?

They are non-overlapping spectral ranges: UV (10–380 nm), visible (380–700 nm), and infrared (700 nm–1000 μm); the <10 nm fraction is also reported if applicable.

Why can I normalize the chart?

Normalization divides each curve by its maximum to compare shapes without the absolute scale dominating.

What units are used in the output?

Mλ is reported in W·m⁻³ (equivalent to W·m⁻²·m⁻¹), with λ in nm or μm depending on your selection.

What are the model limitations?

This is an ideal black-body model; real materials can have emissivity below 1 and specific bands.

Is the integration exact?

A composite numerical integration is used for educational calculations; percentages have a ~1% tolerance.