Calculate Rayleigh range, beam divergence and beam size at any distance for a Gaussian laser beam.
Gaussian-beam model: Rayleigh range zR = π·w0²/(M²·λ), half-angle divergence θ = M²·λ/(π·w0), beam radius w(z) = w0·√(1 + (z/zR)²). Real beams deviate from an ideal Gaussian, so treat results as a design estimate.
Divergence, half-angle (mrad)
How to use this tool
Type the laser wavelength in nanometres — for example 632.8 nm for a red HeNe laser or 1064 nm for Nd:YAG.
Enter w0, the smallest beam radius, in millimetres. Note this is a radius; the tool also reports the diameter.
M² = 1 is a perfect Gaussian beam. Real lasers are worse; use the manufacturer's M² value (often 1.1–2 for good beams).
Enter the distance from the waist and read the Rayleigh range, divergence and the beam radius and diameter there.
Formula & worked example
A 632.8 nm HeNe beam with w0 = 1 mm and M² = 1 has zR ≈ 4.96 m and divergence ≈ 0.201 mrad; at z = 2 m the radius has grown to ≈ 1.078 mm.
Limitations — read this before you rely on it
Ideal Gaussian-beam (paraxial) model. It does not cover astigmatic or top-hat beams, apertures and clipping, atmospheric turbulence, or focusing optics — for a focused spot, apply the same formulas after the lens with the new waist.
Frequently asked questions
The distance from the waist over which the beam radius grows by a factor of √2 (area doubles). Within one Rayleigh range the beam is roughly collimated.
A beam-quality factor: how many times worse a real beam is than a perfect Gaussian beam of the same waist. M² = 1 is diffraction-limited.
This tool reports the half-angle, the standard convention. Double it for the full angle.
Radius. Confusing the two is the most common beam-calculation error, so this tool labels radius and diameter separately everywhere.
Use a shorter focal length, a larger input beam diameter, or a shorter wavelength — spot size scales with λ·f/D.