What is beam divergence?

Beam divergence is the angle at which a laser beam spreads as it propagates. For a Gaussian beam it is characterized by the half-angle theta = lambda / (pi * w0), where lambda is the wavelength and w0 is the beam waist radius.

What is the Rayleigh range?

The Rayleigh range z_R = pi * w0^2 / lambda is the axial distance from the waist at which the beam area doubles (i.e., the radius increases by a factor of sqrt(2)). It separates the near-field region from the far-field.

What is beam waist radius?

The beam waist w0 is the minimum 1/e² intensity radius of the beam, located at the focal point or the output aperture of a well-collimated source. Smaller w0 means larger divergence.

Why does a tighter focus produce more divergence?

This is a consequence of diffraction. A smaller beam waist confines the beam more strongly in the transverse direction, which by Fourier/wave optics means a wider spread of spatial frequencies and therefore a larger divergence angle.

Is this formula valid for all beam types?

The formula applies to the fundamental TEM00 Gaussian mode. Real laser beams may have a beam quality factor M² > 1, which multiplies the divergence angle. Set M² = 1 here for an ideal beam.

Input: wavelength in nanometers, beam waist in micrometers, distance in millimeters. Output: divergence in milliradians and degrees, Rayleigh range in millimeters, beam radius in micrometers.

Beam Divergence Calculator

Name: Beam Divergence Calculator
Availability: InStock
Author: Nham Vu

Calculate the divergence half-angle of a Gaussian laser beam and its radius at any propagation distance from the waist.

Beam Parameters

Wavelength λ (nm)

Common: 405 (violet), 532 (green), 632.8 (HeNe), 1064 (Nd:YAG)

Beam waist radius w₀ (μm)

The minimum 1/e² intensity radius of the beam.

Propagation distance z (mm) — optional

Leave blank to skip beam radius at distance calculation.

Enter wavelength and beam waist to calculate divergence.

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Summary

Calculate the divergence half-angle of a Gaussian laser beam and its radius at any propagation distance from the waist.

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.
All results update instantly as you type.

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: 2026-06-09 · Reviewed by Nham Vu