What is spectral radiance?

Spectral radiance B(λ,T) is the power emitted by a blackbody per unit area of the emitting surface, per unit solid angle, per unit wavelength interval. Its SI unit is W·sr⁻¹·m⁻³ (watts per steradian per cubic meter), which is equivalent to W·sr⁻¹·m⁻²·m⁻¹ when written out explicitly.

What are the physical constants used?

Planck constant h = 6.626×10⁻³⁴ J·s; speed of light c = 2.998×10⁸ m/s; Boltzmann constant k = 1.381×10⁻²³ J/K; Wien displacement constant b = 2.898×10⁻³ m·K.

What is Wien's displacement law?

Wien's displacement law states that the peak emission wavelength of a blackbody is λ_max = b / T, where b = 2.898×10⁻³ m·K. As temperature increases, the peak shifts to shorter (bluer) wavelengths.

Why does B(λ,T) go to zero at very short and very long wavelengths?

At very short wavelengths the exponential term in the denominator grows extremely large, making B vanishingly small. At very long wavelengths the λ⁵ factor in the denominator drives B toward zero as well. The peak between these two limits is what Planck's law predicts exactly.

Does this apply to real objects?

Planck's law is exact for ideal blackbodies. Real objects have emissivity ε < 1, so their actual spectral radiance is ε × B(λ,T). This calculator gives the ideal blackbody value; multiply by emissivity for real surfaces.

What temperature is the Sun?

The Sun's photosphere is approximately 5778 K, giving a peak emission near 501 nm (visible green). The total output follows the Stefan-Boltzmann law: P = σT⁴ per unit area.

Planck Radiation Calculator

Enter a wavelength and temperature to compute spectral radiance using Planck's blackbody radiation law. Also shows Wien's peak wavelength.

Blackbody Parameters

Wavelength λ (nm)

Visible light: 380–700 nm

Temperature T (K)

Must be above 0 K (absolute zero)

Quick Presets

Result

Spectral Radiance B(λ,T)

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W · sr⁻¹ · m⁻³

Peak Wavelength λ_max

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Wien's displacement law

Input λ Region

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Peak λ Region

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Formula

B(λ,T) = (2hc²/λ⁵) × 1/(exp(hc/λkT) − 1)

Peak Wavelengths — Common Temperatures

Source	T (K)	λ_max (nm)	Region

Summary

Planck's radiation law describes how a blackbody emits electromagnetic radiation at every wavelength as a function of temperature. The spectral radiance B(λ,T) gives the power emitted per unit area, per unit solid angle, per unit wavelength. Wien's displacement law gives the wavelength of peak emission directly: λ_max = b / T. This calculator combines both, letting you compute spectral radiance at any wavelength and see where the emission peaks.

How it works

Enter the wavelength λ in nanometers (e.g. 500 nm for visible green light).
Enter the blackbody temperature T in Kelvin (e.g. 5778 K for the Sun).
The calculator computes B(λ,T) = (2hc²/λ⁵) × 1/(exp(hc/λkT) − 1) using the physical constants h, c, and k.
Wien's displacement law (λ_max = 2.898×10⁻³ / T) gives the peak emission wavelength.
The spectral region (UV, visible, infrared, etc.) is identified for both the input wavelength and the peak.
A reference table shows peak wavelengths for several common temperatures.

Use cases

Compute the spectral radiance of the Sun at a specific wavelength for astrophysics problems.
Determine how much radiation a furnace emits at infrared wavelengths.
Verify Planck's law numerical results for thermodynamics coursework.
Compare emission at different temperatures for incandescent bulb design.
Estimate peak emission wavelength for industrial heat sources.
Explore the relationship between temperature and blackbody spectrum shape.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu