Physics

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Laser Beam Divergence Calculator.

Estimate geometric full-angle divergence from beam diameters and propagation distance.

On-device calculationNo signup
01

Set your values

Results update as you type.

fullAngleRad: 0.0002

fullAngleRad

0.000200
Full angle: 0.2 mrad

Full angle

0.200000mrad
Half angle: 0.0001 rad

Half angle

0.000100rad

Results update automatically as you type.

Use Cases

Optical system design

Engineers and researchers use this to estimate how much a laser beam spreads over a given distance, helping to design collimation or focusing optics.

Example: A laser with 2 mm initial diameter expands to 5 mm after 10 m, giving a divergence of about 0.3 mrad.

Beam quality assessment

Compare measured beam diameters at two points to quickly assess if a laser's divergence meets specifications.

Example: Check if a laser's divergence is within the datasheet value by measuring at two distances.

Frequently Asked Questions

What does this calculator estimate?
It estimates the geometric full-angle divergence of a laser beam based on the initial beam diameter, final beam diameter, and the propagation distance between those two points. The result is given in radians (or degrees if you convert).
How is divergence calculated?
The calculator uses the formula: full-angle divergence = 2 * arctan((final diameter - initial diameter) / (2 * distance)). This assumes a linear expansion of the beam over the given distance.
What units should I use?
All inputs must be in meters (m) for consistency. The calculator will output the divergence in radians. You can convert to degrees by multiplying by 180/π.

Tips & Common Mistakes

Tips

  • Ensure both diameter measurements are taken at the same beam cross-section orientation (e.g., 1/e² or full width) for accurate results.
  • Use the same units for all inputs (meters) to avoid conversion errors.
  • For small angles, divergence in radians is approximately equal to (final diameter - initial diameter) / distance, but the calculator uses the exact arctan formula.
  • Measure the propagation distance along the beam axis, not the path length if there are mirrors or lenses.

Common Mistakes to Avoid

  • Using different units for diameters and distance (e.g., mm for diameters and m for distance) without converting.
  • Forgetting that the formula gives full-angle divergence, not half-angle. If you need half-angle, divide the result by 2.
  • Assuming the beam expands linearly even in the near field; this calculator is for geometric divergence, not diffraction-limited divergence.

Last updated: August 13, 2026