Laser Spot Size Calculator

The laser spot size w(z) is the 1/e² beam radius of a Gaussian (TEM00) beam at a distance z from the beam waist: the radius where the intensity falls to 1/e² (≈13.5%) of the peak on-axis intensity. It is a radius, not a diameter — the full spot diameter is 2·w(z).

For an ideal Gaussian beam, w(z) = w₀·√(1 + (z/z_R)²), where w₀ is the beam waist radius and z_R = π·w₀²/λ is the Rayleigh range. This calculator solves the formula in all four directions: spot radius, distance, waist, or wavelength.

With w₀ = 1 mm and λ = 532 nm, the Rayleigh range is z_R = π·(1 mm)²/532 nm ≈ 5.91 m. At z = 10 m (≈1.69 Rayleigh ranges), the spot radius is w ≈ 1.97 mm, so the spot diameter is ≈ 3.93 mm and the beam has expanded ≈1.97×.

The Rayleigh range z_R = π·w₀²/λ is the distance from the waist at which the beam radius grows to √2·w₀ (the beam area doubles). It separates the near field (z ≪ z_R, spot roughly constant) from the far field (z ≫ z_R, spot grows almost linearly with distance).

Spot radius w is the 1/e² radius. Spot diameter is simply 2w. FWHM (full width at half maximum) of the intensity profile is ≈1.1774·w. Example: for the 1 mm / 532 nm beam at 10 m, w ≈ 1.97 mm, diameter ≈ 3.93 mm, FWHM ≈ 2.32 mm.

Yes. Inverting w(z) for w₀ gives a quadratic with up to two physical solutions. Example: measuring w = 2 mm at z = 10 m with λ = 532 nm yields w₀ ≈ 1.75 mm (beam barely expanded) or w₀ ≈ 0.967 mm (tight focus that expanded ≈2.07×). This calculator reports both solutions when they exist.

Far beyond the Rayleigh range (z ≫ z_R), w(z) ≈ w₀·z/z_R = λ·z/(π·w₀), i.e. nearly linear in z. Example: for w₀ = 1 mm, λ = 532 nm, at z = 100 m the exact radius is ≈16.96 mm while the linear approximation gives ≈16.93 mm — within 0.2%.

Spot size w(z) is the beam radius at a specific distance z. Beam divergence θ ≈ λ/(π·w₀) is the far-field half-angle describing how fast the beam spreads. This tool computes size-at-distance; use a beam divergence calculator for the angle itself.

A beam expander multiplies the waist w₀ by its magnification M, which increases the Rayleigh range by M² and shrinks the far-field spot growth proportionally. Enter the expanded waist into this calculator to get the new spot sizes at any distance.

Waist and spot radius: µm or mm; distance: m or km; wavelength: nm or µm. Physically the spot can never be smaller than the waist, so solving for distance or wavelength requires w > w₀, solving for the waist requires z > 0, and no real waist exists if the measured spot is too small for the given distance and wavelength.