Laser Beam Divergence Calculator

Laser beam divergence describes how much the beam expands as it travels away from the source. It is typically expressed as a half-angle (the angle between the beam axis and the edge of the expanding cone) in milliradians (mrad) or degrees. Even highly collimated laser beams diverge slightly due to the wave nature of light.

The standard formula for the half-angle divergence is: θ = arctan((D₂ − D₁) / (2 × L)), where D₁ and D₂ are the beam diameters at two points and L is the distance between those points. This calculator uses that exact formula, assuming a Gaussian TEM₀₀ beam profile.

The half-angle divergence is the angle between the optical axis and one edge of the beam cone. The full-angle divergence is simply twice the half-angle and represents the total angular spread of the beam. Many manufacturers and datasheets specify the full-angle, so always check which convention is being used.

The most effective way to reduce divergence is to increase the beam diameter at the output aperture using a beam expander. Because divergence is inversely proportional to beam waist size (θ ≈ λ / (π·w₀) for a Gaussian beam), a larger initial beam diameter produces a smaller divergence angle. Higher beam quality (M² closer to 1) also reduces divergence.

Even a low-divergence laser beam (e.g. 1 mrad half-angle) expands to roughly 384 km in diameter at the Moon's distance of ~384,000 km. The intensity drops so dramatically that the beam becomes undetectable. Only powerful pulsed lasers with extremely narrow divergence and large aperture telescopes can achieve lunar ranging experiments.

This calculator assumes the laser operates as an ideal TEM₀₀ Gaussian beam with constant divergence along the propagation path. It also assumes the beam travels through a single homogeneous, isotropic medium. In real-world setups with optical elements, turbulence, or higher-order modes, actual divergence may differ.

The calculator outputs divergence in milliradians (mrad), radians (rad), and degrees (°). Milliradians are the most common unit for specifying laser beam divergence in engineering and industrial contexts, while degrees may be more intuitive for general audiences.

Using the beam diameter mode, you can input your initial beam diameter and half-angle divergence to find the beam size at any propagation distance. The formula used is: D(z) = 2 × z × tan(θ) + D₀, where θ is the half-angle, z is the distance, and D₀ is the initial diameter.