Laser Brightness Calculator
Free calculate laser radiance (brightness) from power, beam diameter, and divergence angle. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
Full divergence angle (edge to edge)
Results
Enter parameters to calculate
What is Laser Brightness (Radiance)?
Laser brightness, also called radiance, is a measure of how much power a laser emits per unit area per unit solid angle. It quantifies the "brightness" or intensity concentration of a laser beam.
Radiance is measured in W/(m²·sr), where sr is steradians (unit of solid angle). High radiance means the laser concentrates a lot of power in a small area with small divergence - this is what makes lasers so useful for focusing and precision applications.
Radiance is a fundamental property that determines how well a laser can be focused. Higher radiance lasers can be focused to smaller spots with higher power density, making them ideal for cutting, welding, and other high-intensity applications.
Radiance Formula
Where:
- • L = Radiance (W/(m²·sr))
- • P = Laser power (W)
- • A = Beam cross-sectional area (m²) = π(D/2)²
- • Ω = Solid angle (sr) ≈ πθ² for small angles
- • D = Beam diameter (m)
- • θ = Full divergence angle (rad)
For small divergence angles:
L = P / (π(D/2)² × πθ²) = 4P / (π²D²θ²)
How to Calculate
-
1
Convert all units to SI
Convert power to watts, diameter to meters, divergence to radians.
-
2
Calculate beam area
A = π(D/2)² = πD²/4
-
3
Calculate solid angle
Ω ≈ πθ² for small divergence angles (θ in radians).
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4
Calculate radiance
L = P / (A × Ω)
Practical Examples
Example 1: Low Power Laser
1 mW laser, 1 mm diameter, 1 mrad divergence. Calculate radiance.
Solution:
A = π(0.001/2)² = 7.85×10⁻⁷ m²
Ω = π(0.001)² = 3.14×10⁻⁶ sr
L = 0.001 / (7.85×10⁻⁷ × 3.14×10⁻⁶) ≈ 4.05×10⁸ W/(m²·sr)
Example 2: High Power Laser
10 W laser, 5 mm diameter, 0.5 mrad divergence.
Solution:
A = π(0.005/2)² = 1.96×10⁻⁵ m²
Ω = π(0.0005)² = 7.85×10⁻⁷ sr
L ≈ 6.5×10¹¹ W/(m²·sr) (much brighter!)
Applications
Material Processing
High radiance enables precise cutting, welding, and drilling by focusing high power into small spots.
Medical Lasers
High brightness allows precise tissue ablation, surgery, and therapeutic applications with minimal collateral damage.
Optical Communications
High radiance enables long-distance free-space optical links with minimal beam spread and high signal strength.
Research
Characterizing laser performance, comparing different laser types, and optimizing beam parameters for experiments.
Frequently Asked Questions
What is the difference between radiance and irradiance?
Radiance (L) is power per unit area per unit solid angle (W/(m²·sr)). Irradiance (E) is power per unit area (W/m²). Radiance includes the angular distribution, making it more fundamental for characterizing sources.
Why is radiance important?
Radiance is conserved in optical systems (can't increase it). It determines the maximum power density achievable when focusing. Higher radiance means better focusability and more intense spots.
How does beam quality affect radiance?
Better beam quality (lower M²) means smaller divergence for the same beam diameter, resulting in higher radiance. Ideal Gaussian beams (M²=1) have maximum radiance for given power and diameter.
Can radiance be increased?
Radiance cannot be increased by passive optics (conservation law). However, you can increase power, reduce beam diameter, or improve beam quality (lower M²) to increase radiance at the source.
What is a typical radiance value?
Typical values range from 10⁶-10¹² W/(m²·sr) for common lasers. High-power industrial lasers can reach 10¹³-10¹⁴ W/(m²·sr). The sun has radiance ~2×10⁷ W/(m²·sr) for comparison.