Science

Planck Blackbody Calculator

Calculate the peak emission wavelength using Wien's law and total radiated power using the Stefan-Boltzmann law. Enter any temperature to get instant results with step-by-step working.

planck-blackbody-calculator
Peak wavelength (Wien's law)
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Temperature—
Spectral region—
Total power / area (σT⁴ε)—
Power for 1 m² surface—
Wien's law working—
Stefan-Boltzmann working—

Key formulas

Wien's displacement law: λ_max = b / T b = 2.897 × 10⁻³ m·K Stefan-Boltzmann law: P/A = ε σ T⁴ σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴ ε = emissivity (1 for blackbody) T must be in Kelvin: K = °C + 273.15

Blackbody temperatures — reference

ObjectTemperature (K)Peak wavelength
Human body3109.35 µm
Light bulb filament2,8001.04 µm
Sun surface5,778502 nm
Lightning bolt~30,000~97 nm
X-ray star~10⁷~0.3 nm

Worked examples

Example 1 — Peak wavelength of the Sun (5778 K):

λ_max = b/T = 2.897×10⁻³ / 5778 = 5.01×10⁻⁷ m = 501 nm (green) The Sun peaks in green but appears white because it emits across all visible wavelengths

Example 2 — Power from human skin (T = 310 K, ε = 0.98):

P/A = ε σ T⁴ = 0.98 × 5.67×10⁻⁸ × 310⁴ = 513 W/m² Body surface area ≈ 1.7 m² → total emission ≈ 870 W (offset by radiation absorbed from the environment)

Applications of blackbody radiation

Stellar temperature: Astronomers use Wien's law to estimate stellar surface temperatures from peak emission wavelength. Blue O-type stars (> 30,000 K) peak in UV; red M-type stars (< 3,500 K) peak in near-IR. The colour of a star directly reveals its temperature.

Infrared thermometry: Non-contact thermometers measure emitted IR and apply the Stefan-Boltzmann law to calculate temperature without touching the object — used in industrial furnace monitoring, medical fever screening, and building energy audits.

Cosmic Microwave Background: The CMB is blackbody radiation at 2.725 K — the afterglow of the Big Bang. Its near-perfect blackbody spectrum, measured by COBE and Planck satellites, is one of the strongest confirmations of the Big Bang model.

Blackbody temperatures reference table

ObjectTemperaturePeak λ
CMB2.7 K1.06 mm
Human skin305 K9.5 µm
Incandescent bulb2,800 K1.03 µm
Sun5,778 K501 nm
Blue supergiant30,000 K97 nm

Common questions

  • A blackbody is an idealised object that absorbs all incident radiation and emits radiation purely based on its temperature. The spectrum of emitted radiation — its intensity at each wavelength — is described by Planck's law. Real objects approximate blackbodies to varying degrees (emissivity ε, where ε=1 is a perfect blackbody).
  • Wien's displacement law states that the peak wavelength of blackbody radiation is inversely proportional to the temperature: λ_max × T = b, where b = 2.897 × 10⁻³ m·K (Wien's constant). The Sun (surface ≈ 5778 K) peaks at about 502 nm — green light — though it appears white because it emits strongly across all visible wavelengths.
  • The Stefan-Boltzmann law gives the total power radiated per unit area by a blackbody: P/A = σT⁴, where σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴ is the Stefan-Boltzmann constant. Total radiated power scales with the fourth power of temperature — doubling temperature increases power by 16×.
  • Objects begin to emit visible red light at around 800–900 K (527–627°C). At 1000 K they glow dull red-orange. At 3000 K (like a tungsten filament) they appear orange-white. The Sun at 5778 K emits strongly across all visible wavelengths, appearing white to our eyes.
  • The human body at 37°C (310 K) radiates primarily in the mid-infrared. Using Wien's law: λ_max = 2.897 × 10⁻³ / 310 ≈ 9.35 µm. This is why infrared cameras can detect people — the peak emission is in the thermal infrared range (8–14 µm) that IR sensors detect.