# Blackbody Radiation Curve - Planck's Law, Wien Peak & Color

> Plot Planck blackbody curves for several temperatures with Wien peaks, σT⁴ power, visible fraction, blackbody colour and the Rayleigh–Jeans comparison.

- URL: https://qilingtools.com/en/math/blackbody
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Compare the Planck spectral radiance of the Sun, Sirius, an incandescent bulb, molten lava, the human body or the cosmic microwave background on one chart; the axes switch to logarithmic when the temperatures are far apart, and the visible band is shaded in rainbow colours. Each curve marks its Wien peak, hovering reads the radiance at any wavelength, and dragging a peak or pressing “Sweep temperature” shows the peak sliding to shorter wavelengths as the colour goes from dull red to blue-white. The blackbody colour comes from integrating the spectrum against the CIE 1931 colour-matching functions, alongside σT⁴ exitance, visible fraction and luminous efficacy, and a radius input gives a star’s luminosity from L = 4πR²σT⁴.

## How to use

1. Add presets such as the Sun, a light bulb or the human body, or type any temperature in kelvin (up to six curves)
2. Select a curve and adjust it with the temperature slider or by dragging its peak; switch to log axes if needed
3. Hover to read radiance at any wavelength and turn on the Rayleigh–Jeans curve to see the ultraviolet catastrophe
4. Read the blackbody colour, Wien peak, radiated power and visible fraction, and enter a radius for the luminosity

## Features

- Multiple Planck curves, linear or log axes, rainbow visible band
- Wien peak markers, drag-to-set temperature and an animated temperature sweep
- Hover readout of every curve at any wavelength
- Rayleigh–Jeans and Wien approximations to show the ultraviolet catastrophe
- Blackbody colour from CIE 1931 integration, chromaticity and luminous efficacy
- σT⁴ exitance, UV/visible/IR fractions and stellar luminosity L = 4πR²σT⁴

## FAQ

### What is a blackbody, and are the Sun and the human body blackbodies?

A blackbody is an ideal object that absorbs all radiation falling on it, so its thermal emission depends only on its temperature and follows Planck’s law. Real objects emit the blackbody spectrum multiplied by an emissivity between 0 and 1. The Sun’s photosphere is close to a 5772 K blackbody. Human skin has an infrared emissivity of about 0.98 — nearly ideal — with its peak near 9.3 μm, which is exactly where thermal cameras and forehead thermometers work. The cosmic microwave background, at 2.725 K, is the most perfect blackbody spectrum ever measured.

### What does Wien’s displacement law tell us?

The peak wavelength of blackbody emission is inversely proportional to temperature: λmax = b/T with b ≈ 2.898 × 10⁻³ m·K. A 2700 K bulb peaks around 1.07 μm in the infrared, the Sun near 500 nm in blue-green, and a 10,000 K blue-white star in the ultraviolet. That’s why heated iron glows dull red, then orange, then white, and why astronomers can read a star’s surface temperature from its colour. Plotted per unit frequency, the peak is at νmax ≈ 5.879 × 10¹⁰ Hz/K × T, which is not the same point as c/λmax.

### What was the ultraviolet catastrophe and how did Planck solve it?

Classical physics with equipartition gave the Rayleigh–Jeans law B_λ = 2ckT/λ⁴, which matches experiments at long wavelengths but grows without limit at short ones, so the total radiated energy would be infinite. In 1900 Planck assumed oscillators can only hold energy in multiples of hν, which gives B_λ = 2hc²/λ⁵ · 1/(e^(hc/λkT) − 1). It reduces to Rayleigh–Jeans at long wavelengths, while the exponential suppresses the short-wavelength end. Energy quantisation was the start of quantum mechanics. Turn on the Rayleigh–Jeans curve to watch it shoot upward in the UV.

### Why are incandescent bulbs so inefficient?

A blackbody radiates σT⁴ watts per square metre, but at 2700 K only about 8% of it lands between 380 and 780 nm; more than 90% is infrared heat, so the luminous efficacy is only around 12 lm/W. Even an ideal blackbody peaks at roughly 95 lm/W, near 6600 K. LEDs don’t rely on thermal emission and exceed 150 lm/W, so they need about a tenth of the power for the same light. The tool shows the visible fraction and luminous efficacy at any temperature.

### How is the displayed blackbody colour calculated?

The Planck spectrum is integrated against the CIE 1931 standard observer’s x̄, ȳ and z̄ colour-matching functions from 380 to 780 nm to get the tristimulus values XYZ and the chromaticity (x, y), then converted with the sRGB matrix and gamma. Only the hue is shown; brightness is normalised. Below about 800 K, the Draper point, the visible output is so weak that the object looks black in the dark, so the tool flags it as having no visible glow. Very blue or very red colours outside the sRGB gamut are slightly desaturated.

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