Laser Brightness (Radiance) Calculator
Enter laser power, 1/e² beam radius at the waist, far-field half-angle divergence and M² to calculate brightness (radiance), peak intensity and beam parameter product.
W
mm
mrad
B = P / (A × Ω) = P / (π·w² × π·θ²)
- 1
Beam area A = π × w²
π × 0.001² = 0.000003Emitting area at the 1/e² beam waist radius w (in m²). - 2
Solid angle Ω = π × θ²
π × 0.001² = 0.000003 - 3
Brightness (W/m²·sr)
1 ÷ (0.000003 × 0.000003) = 101,321,183,642.338 - 4
Brightness (W/cm²·sr)
101,321,183,642.338 × 10⁻⁴ = 10,132,118.364
How does this calculator work?
Laser brightness (radiance) is B = P/(π²·w²·θ²) in W/(m²·sr), where w is the 1/e² beam waist radius and θ is the far-field half-angle divergence. The beam parameter product BPP = w·θ is conserved by passive optics. Peak intensity at the waist is I₀ = 2P/(π·w²).
Formula
How this is calculated
Laser brightness, also called radiance, is the power per unit emitting area per unit solid angle: B = P/(A·Ω). For a circular Gaussian beam with 1/e² radius w at the waist, the emitting area is A = π·w², and the far-field solid angle subtended by the half-angle divergence θ is Ω = π·θ². So B = P/(π²·w²·θ²). The higher the brightness, the more power can be focused onto a small area from a given solid angle — this is why brightness determines the achievable focused intensity in laser cutting, pumping, or coherent sources.
The beam parameter product (BPP = w·θ, in mm·mrad) is a conserved quantity in ideal optical systems (a consequence of the brightness theorem / Liouville's theorem). A diffraction-limited Gaussian beam has the minimum possible BPP = λ/π. Real beams have BPP = M²·λ/π, and M² cannot be reduced by any passive optic — it can only be increased by aberrations or scattering. The M² field here lets you compute brightness directly from measured beam parameters without needing wavelength.
The peak intensity at the waist I₀ = 2P/(π·w²) is the on-axis intensity for a Gaussian beam. The range-meter shows where your beam falls in the spectrum from LED-like sources (low brightness) to high-power pulsed lasers (extreme brightness).
Frequently asked questions
Intensity (irradiance) is power per unit area (W/cm²) — it depends on how tightly you focus the beam. Brightness (radiance) is power per unit area per unit solid angle (W/(cm²·sr)) — it is an intrinsic property of the source that cannot be increased by lenses. Focusing a beam increases intensity but does not change brightness.
Liouville's theorem (or the brightness theorem) states that a passive optical system cannot increase the phase-space density of a beam. A lens that decreases the spot size by a factor k must increase the divergence by k, leaving the product A·Ω (and hence brightness) unchanged or reduced. Only the laser gain medium can increase brightness.
Single-mode fibre lasers at 1064 nm typically have BPP ≈ 0.3–0.4 mm·mrad, very close to the diffraction limit λ/π ≈ 0.34 mm·mrad (M² ≈ 1.1). Industrial multi-kW fibre lasers with 50 µm core diameter can have BPP of 2–4 mm·mrad.
Also known as
TG we-Calculate Editorial Team. (2026). Laser Brightness (Radiance) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/laser-brightness-calculator
TG we-Calculate Editorial Team. "Laser Brightness (Radiance) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/laser-brightness-calculator.
TG we-Calculate Editorial Team, "Laser Brightness (Radiance) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/laser-brightness-calculator
@misc{wecalculate_laser_brightness_calculator, title = {Laser Brightness (Radiance) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/laser-brightness-calculator}}, year = {2026}, note = {TG we-Calculate} }
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