Beam Divergence Calculator
Calculate the divergence half-angle of a Gaussian laser beam and its radius at any propagation distance from the waist.
Use the Beam Divergence Calculator
Beam Parameters
Common: 405 (violet), 532 (green), 632.8 (HeNe), 1064 (Nd:YAG)
The minimum 1/e² intensity radius of the beam.
Leave blank to skip beam radius at distance calculation.
Enter wavelength and beam waist to calculate divergence.
Divergence & Rayleigh Range
Half-angle (mrad)
—
Half-angle (deg)
—
Full-angle (mrad)
—
Rayleigh range zR
—
mm
Beam Radius at Distance z
Beam radius w(z)
—
μm
Radius / waist ratio
—
w(z) / w₀
Formulas Used
- θ = λ / (π · w₀) — far-field half-angle (rad)
- zR = π · w₀² / λ — Rayleigh range
- w(z) = w₀ · √(1 + (z/zR)²) — beam radius at z
Valid for ideal TEM₀₀ Gaussian beams (M² = 1).
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Summary
This tool computes the far-field divergence half-angle of a Gaussian laser beam using the standard formula theta = lambda / (pi * w0), where lambda is the wavelength and w0 is the beam waist radius. It also calculates the beam radius w(z) at any axial distance z, accounting for the Rayleigh range. Results are displayed in both milliradians and degrees.
How it works
- Enter the laser wavelength in nanometers (e.g., 632.8 nm for a HeNe laser).
- Enter the beam waist radius (the minimum 1/e² intensity radius) in micrometers.
- Optionally enter a propagation distance in millimeters to compute the beam radius at that point.
- The calculator derives the Rayleigh range, divergence half-angle, and beam radius at the given distance.
- Click Calculate or press Enter to update the results.
Use cases
- Design collimated laser optics for experiments or industrial systems.
- Estimate spot size at the focal plane of a focusing lens.
- Verify beam propagation models against analytical Gaussian optics.
- Size beam expanders to reduce divergence for long-range applications.
- Teach or study Gaussian beam propagation in optics courses.
- Evaluate fiber coupling efficiency by matching mode field diameters.
Frequently Asked Questions
Last updated: 2026-05-28 · Reviewed by Nham Vu