Color Temperature Calculator & Black Body Radiation

simulator intermediate ~8 min
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5500K — daylight white

5500K approximates direct sunlight color temperature. Peak emission is at 527nm (green). The sun's surface temperature of 5778K produces the white light we perceive as neutral.

Formula

Wien's law: λ_max = 2,897,772 / T (nm·K)
Planck's law: B(λ,T) = (2hc²/λ⁵) · 1/(e^(hc/λkT) − 1)
Stefan-Boltzmann: P = σ·T⁴ where σ ≈ 5.67×10⁻⁸ W·m⁻²·K⁻⁴

When Heat Becomes Light

Every hot object glows. Heat a piece of iron and it shifts from invisible infrared to dull red, bright orange, yellow-white, and eventually blue-white. This progression follows Planck's law of black body radiation — one of the foundational equations of quantum mechanics. Max Planck derived it in 1900 by proposing that energy is quantized, inadvertently launching the quantum revolution. This simulation lets you see the black body spectrum at any temperature and watch how it maps to perceived color.

Wien's Displacement Law

Wien's law provides an elegant shortcut: the peak wavelength of emission is inversely proportional to temperature. At 3000K (incandescent bulb), the peak is at 966nm — deep in the infrared, with only the tail of the distribution in the visible range, producing warm yellow light. At 5800K (the sun), the peak is at 500nm, right in the green part of the visible spectrum. At 10000K, the peak shifts to 290nm in the ultraviolet, and the visible emission skews blue.

Color Temperature in Daily Life

The concept of color temperature is everywhere in modern life. Light bulb packaging lists it in Kelvin: 2700K for warm white, 4000K for neutral, 6500K for daylight. Camera white balance settings use color temperature to correct for ambient lighting. Display calibration targets 6500K (D65) as the standard white point. Your phone's "night mode" reduces color temperature in the evening, shifting from blue-white to amber to reduce melatonin suppression and improve sleep quality.

Beyond Ideal Black Bodies

Real light sources deviate from perfect black body spectra. Fluorescent lights have spiky emission from mercury vapor and phosphors. LEDs combine a blue pump with yellow phosphor, creating a two-peaked spectrum. These deviations are quantified by correlated color temperature (CCT) — the black body temperature whose perceived color most closely matches the light source — and by Duv, which measures distance from the Planckian locus in chromaticity space. Together, CCT and Duv fully characterize a light source's color appearance.

FAQ

What is color temperature?

Color temperature describes the color appearance of light by comparing it to a theoretical black body heated to a specific temperature in Kelvin. Lower temperatures (2000–3000K) produce warm reddish-yellow light like candles. Higher temperatures (5000–6500K) produce neutral white daylight. Very high temperatures (8000K+) produce cool blue light.

What is black body radiation?

A black body is an idealized object that absorbs all incoming radiation and re-emits it based solely on its temperature. Planck's law describes the spectral distribution of this emission. As temperature rises, the peak wavelength shifts from infrared through red, orange, yellow, white, to blue — following Wien's displacement law: λ_max = 2,897,772/T nm.

Why does the sun appear yellow but has a temperature of ~5778K (white)?

The sun is actually white when viewed from space. It appears yellow from Earth because Rayleigh scattering in the atmosphere removes short (blue) wavelengths. At sunrise and sunset, the longer atmospheric path scatters even more blue light, making the sun appear orange or red. The color temperature of direct sunlight at noon is approximately 5500K.

How is color temperature used in lighting and photography?

Photographers use color temperature for white balance — ensuring whites look white under any lighting. Lighting designers specify color temperature to set mood: warm 2700K for restaurants, neutral 4000K for offices, cool 6500K for hospitals. LED and display manufacturers tune phosphors to achieve target color temperatures.

Sources

Embed

<iframe src="https://homo-deus.com/lab/color-science/color-temperature/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub