Calculate Color Temperature

Wien's displacement law for temperature and peak wavelength

Color Temperature Calculator (JavaScript)

Wien's law

For blackbody radiation, λmax·T = b with b = 2.897771955·10⁻³ m·K.

Result

Example calculations

Example 1: Solar surface

Given: T = 5778 K

\[\lambda_{max}=\frac{b}{T}=\frac{2.8978\cdot10^{-3}}{5778}\approx5.01\cdot10^{-7}\,m\]

Result: λmax ≈ 501 nm

Example 2: Incandescent lamp

Given: T = 2700 K

\[\lambda_{max}=\frac{2.8978\cdot10^{-3}}{2700}\approx1.073\cdot10^{-6}\,m\]

Result: λmax ≈ 1073 nm (near infrared)

Example 3: Temperature from λmax

Given: λmax = 650 nm

\[T=\frac{b}{\lambda_{max}}=\frac{2.8978\cdot10^{-3}}{6.5\cdot10^{-7}}\approx4458\,K\]

Result: T ≈ 4458 K

Formulas and comprehensive description

Wien's displacement law describes the relation between blackbody temperature and wavelength of maximum emission. Higher temperatures shift the maximum toward shorter wavelengths. This is central for astrophysics, spectral analysis, and lighting engineering.

Wien law
\[\lambda_{max}\cdot T=b\]
Temperature
\[T=\frac{b}{\lambda_{max}}\]
Peak wavelength
\[\lambda_{max}=\frac{b}{T}\]
Displacement constant
\[b=2.897771955\cdot10^{-3}\,m\,K\]
Practical relevance
Warm light sources (lower Kelvin) emit stronger in red/IR regions, while hot sources (higher Kelvin) shift toward blue/UV. Stellar color can therefore be used as an approximate temperature indicator.

Description

What is Color Temperature?

Color temperature is a measure of the color of light emitted by a radiation source. It is based on the physical property that hot objects (blackbodies) emit light in various colors. Color temperature is measured in Kelvin (K) and describes the temperature at which an ideal blackbody would emit light of the same color as the observed light source.

Wien's Displacement Law

Wien's displacement law (named after Wilhelm Wien) describes the fundamental relationship between the temperature of an ideal radiator and the wavelength of its maximum radiation:

\[λ_{max} \cdot T = b\]
  • λmax – wavelength of maximum radiation in meters (m)
  • T – absolute temperature in Kelvin (K)
  • b – Wien's displacement constant ≈ 2.898 × 10⁻³ m·K
Physical Interpretation

The higher the temperature, the shorter the wavelength of maximum radiation:

  • Low temperatures (1000–3000 K): Maximum in red/infrared range → warm, reddish light (e.g., incandescent bulbs)
  • Medium temperatures (4000–6000 K): Maximum in yellow-white range → neutral light (e.g., sunlight, 5778 K)
  • High temperatures (7000–10000 K): Maximum in blue range → cool, bluish light (e.g., clear sky)
  • Very high temperatures (>10000 K): Maximum in UV range → very blue light (e.g., hot stars)
Typical Color Temperatures of Light Sources
Light Source Color Temperature (K) Characterization
Candlelight 1900 K Very warm, deep orange
Incandescent bulb (40W) 2500 K Warm, yellow-orange
Incandescent bulb (100W) 2700 K Warm, yellow
Halogen lamp 3200 K Warm-white
Daylight (9 AM, 3 PM) 4000–5000 K Neutral-white
Sunlight (Noon) 5778 K Neutral-white
Overcast sky 6500 K Cool-white
Clear sky (Noon) 7500 K Bluish-white
Clear sky (Horizon) 10000 K Strongly bluish
Practical Applications
  • Photography and film: White balance is adjusted to match the color temperature of the light source
  • Lighting engineering: Selection of lamps for different rooms and moods
  • Astronomy: Determination of stellar surface temperature (e.g., Sun: 5778 K, red giants: 3000 K, blue supergiants: >30000 K)
  • Thermography: Temperature measurement via infrared radiation
  • Display technology: Color temperature settings for screens and monitors
Notes on Blackbody Assumption

Wien's displacement law applies exactly to ideal blackbodies. Real light sources deviate from this, but generally follow this law approximately. Phosphors and LED lamps can have artificially generated color temperatures that do not correspond to thermal radiation, but are still specified in Kelvin (correlated color temperature).

Note
Color temperature is not identical to the actual physical temperature of a light source. For example, an LED can have a color temperature of 5000 K while operating at room temperature. Color temperature only describes the color of the emitted light.
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