Laser Brightness Calculator (radiance from power, wavelength and M²)

Understanding the laser brightness calculator — concept and principle

This calculator finds the brightness, or radiance, of a laser beam: its optical power per unit area per unit solid angle. It uses the power, wavelength and beam quality M² on both axes, and also gives the beam parameter product and how close the beam is to the diffraction-limited ideal. It helps compare laser sources for cutting, pumping or long-range applications.

Brightness is power per area per solid angle; beam quality squared sets how far below the ideal it falls.

How it is calculated

B = P ÷ (λ² × M²x × M²y), in W/(m²·sr)

Beam parameter product (per axis) = w₀ θ = M² λ ÷ π

Diffraction-limited brightness (M² = 1) = P ÷ λ²

Share of the ideal = 100% ÷ (M²x × M²y)

P in watts, λ in nm; results in MW/(cm²·sr) and TW/(m²·sr).

The principle

A beam's waist has area πw₀² and its far-field cone has solid angle πθ². Radiance is power divided by both. For a Gaussian-like beam the product w₀θ is fixed by the beam quality, M²λ/π, so the radiance depends only on power, wavelength and M². Lenses can trade a smaller spot for a wider angle, but they cannot increase radiance; it is conserved through ideal optics. That makes brightness the right figure for comparing how well different sources can be focused or sent over long distances.

Worked example

Default inputs: P = 1 W, λ = 532 nm, M²x = M²y = 1.1.

λ² = (532 × 10⁻⁹)² = 2.830 × 10⁻¹³ m².
B = 1 ÷ (2.830 × 10⁻¹³ × 1.21) = 2.920 × 10¹² W/(m²·sr) = 2.9201 TW/(m²·sr) = 292.01 MW/(cm²·sr).
Beam parameter product = 1.1 × 532 × 10⁻⁹ ÷ π = 0.1863 mm·mrad on each axis.
With M² = 1: 353.33 MW/(cm²·sr); share of ideal = 100 ÷ 1.21 = 82.64%.

Each point is the calculator re-run with only “Wavelength (nm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Wavelength (nm)	Radiance (MW per cm² per steradian)
133	4,672.09
266	1,168.02
399	519.12
532	292.01
665	186.88
798	129.78
1,064	73

How to read the result

Brightness rises with power and falls with the square of the wavelength and with poorer beam quality on either axis. A beam with M² = 2 on both axes has only a quarter of the ideal brightness. Use the figure to compare sources; it is not an eye-safety limit.

Common mistakes

Treating power alone as a measure of how intense a focused spot can be.
Forgetting that M² can differ between the two axes, as in many diode lasers.
Expecting optics to increase brightness.

Keep in mind: Brightness is a comparison figure, not a safety limit. Follow the laser safety rules for your laser class and wavelength.

Frequently asked questions

Can a lens make a beam brighter?

No. Ideal passive optics conserve radiance; they only trade spot size for angle.

Why does a shorter wavelength give higher brightness?

Its diffraction-limited beam parameter product is smaller.

What is the beam parameter product?

Waist radius times far-field half-angle, M²λ/π for each axis.

Why do diode lasers have lower brightness?

Their beams usually have high M², especially along the slow axis.

Sources: R. Paschotta, RP Photonics Encyclopedia, "Brightness" and "M² factor"

Checked 9 Nov 2026. RP Photonics Encyclopedia (R. Paschotta): “Brightness” (radiance = optical power per unit area and solid angle; beam quality and power determine brightness) and “M² factor” (θ = M²λ/(πw₀), beam parameter product = M² × λ/π). Small-angle cone solid angle πθ² — standard geometry.

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