How to use it
- Choose whether to find the peak wavelength or the temperature.
- Enter the temperature in K or °C, or the peak wavelength in nm or µm.
- Set the emissivity (1 for an ideal black body, less for real surfaces) and the radiating area.
- Read the peak wavelength or temperature, the frequency peak and the radiated power.
Formulas
- Wien’s displacement law: λ_max = b ÷ T, b = 2.897771955 × 10⁻³ m·K
- Temperature from the peak: T = b ÷ λ_max
- Frequency peak: ν_max = 5.878925757 × 10¹⁰ Hz/K × T
- Stefan–Boltzmann law: M = ε σ T⁴, P = M × A, σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴)
Worked example
The Sun, T = 5778 K: λ_max = 2.897771955 × 10⁻³ ÷ 5778 = 501.52 nm. One square metre radiates 5.670374419 × 10⁻⁸ × 5778⁴ = 63,200,699.73 W/m², about 63.2 MW.
Human skin at 34 °C (307.15 K) with ε = 0.98: λ_max = 9.4344 µm, in the far infrared – which is why thermal cameras work at 8–14 µm. 1.8 m² of skin radiates 890.25 W (and absorbs most of that back from the surroundings).
A spectrum peaking at 10 µm belongs to a body at T = 2.897771955 × 10⁻³ ÷ 10⁻⁵ = 289.78 K (16.63 °C).
Tips
- Use kelvin inside the formulas. Picking °C here adds 273.15 for you.
- Real objects are not perfect black bodies. Emissivity changes the power but, for a grey body, not the peak.
- Net heat loss is lower than the total. A body also absorbs radiation from its surroundings; the net loss is ε σ A (T⁴ − T_surroundings⁴).