Blackbody Peak Wavelength Calculator (Wien's Law)
Calculate the peak emission wavelength of a blackbody radiator from its temperature.
Identify the color of thermal radiation and total radiated power.
Peak Wavelength
Every object with temperature above absolute zero emits thermal radiation. The wavelength at which emission is maximum is given by Wien’s Displacement Law:
λ_max = b / T
Where:
- λ_max = Peak wavelength (meters)
- b = Wien’s displacement constant = 2.898 × 10⁻³ m·K
- T = Absolute temperature (Kelvin)
Total radiated power (Stefan-Boltzmann Law): P = σ × A × T⁴ σ = 5.67 × 10⁻⁸ W/(m²·K⁴) (Stefan-Boltzmann constant)
Temperature-color relationship:
| Temperature | Peak λ | Appearance |
|---|---|---|
| 1,000 K | 2,900 nm | Deep red glow |
| 3,000 K | 966 nm | Red-orange (incandescent bulb) |
| 5,778 K | 501 nm | Bright white-green (Sun) |
| 10,000 K | 290 nm | Blue-white |
| 30,000 K | 97 nm | UV (hot stars) |
| 2.73 K | 1.06 mm | Cosmic microwave background |
Applications:
- Photography: Color temperature (measured in Kelvin) describes the “warmth” of light sources
- Astronomy: Star temperatures are measured from their spectral peak (O-type stars >30,000 K, M-type stars ~3,000 K)
- Thermal cameras: Detect IR radiation (λ > 700 nm) from objects at room temperature (~300 K, peak at 9.7 μm)
- Incandescent bulbs: Most energy emitted as IR (heat), not visible light — hence they are inefficient