Planck Radiation Calculator
Enter temperature to compute the total radiance and peak wavelength via the Stefan–Boltzmann law and Wien's displacement law.
Input Data
Results
At a glance:A blackbody emits a continuous spectrum described by Planck's law. Two key results: the total emitted radiance (power per area) is the Stefan–Boltzmann law L = σ·T⁴ with σ = 5.670374×10⁻⁸ W/(m²·K⁴), and the wavelength of peak emission follows Wien's displacement law λ_max = b/T with b = 2.8977719×10⁻³ m·K. Hotter objects emit more total power (∝T⁴) and at shorter wavelengths (∝1/T). At 300 K the peak is ~9.7 µm (infrared); at 5800 K (Sun) ~0.50 µm (visible green). This tool returns L and λ_max from T (and reports σ and b).
Formula
Stefan–Boltzmann: L = σ·T⁴
Wien's law: λ_max = b/T
σ = 5.67×10⁻⁸, b = 2.898×10⁻³
$$j^* = \sigma T^4, \quad \sigma = \frac{2\pi^5 k^4}{15 h^3 c^2}$$$$\lambda_{\max} = \frac{b}{T}, \quad b \approx 2.898 \times 10^{-3}\ \mathrm{m\cdot K}$$How to Use
- Enter the temperature T (K).
- The calculator returns total radiance and peak wavelength (µm and m).
Case Studies
Sun's spectrum
T = 5800 K.
L = 5.67e-8×5800⁴ ≈ 6.4×10⁷ W/m².
λ_max = 2.898e-3/5800 ≈ 0.50 µm (green).
FAQ
Why does peak wavelength shift with temperature?
Wien's law λ_max = b/T: as T rises the spectrum shifts to shorter (bluer) wavelengths — the reason heated metal glows red then white.
What is the Stefan–Boltzmann constant?
σ = 5.67×10⁻⁸ W/(m²·K⁴); it sets how fast a blackbody radiates per unit area as the fourth power of temperature.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.