Laser Beam Parameters Calculator
Calculate Gaussian laser beam parameters: Rayleigh range, far-field divergence and beam radius at a distance from the waist, with an M² beam-quality factor for real beams.
Last updated: October 2026
Result
1,241.15 mm
Formula below · 2 sources (laserbeamsize.readthedocs.io, ophiropt.com) · Updated Oct 2026
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About this calculator
A laser beam is narrowest at its waist, where its 1/e² radius is w₀. For an ideal Gaussian beam of wavelength λ:
Rayleigh range: z_R = π w₀² ÷ λ Half-angle divergence: θ = λ ÷ (π w₀) Beam radius at distance z: w(z) = w₀ √(1 + (z ÷ z_R)²)
Within one Rayleigh range of the waist the beam stays nearly collimated: at z = z_R its radius has grown by √2 and its area has doubled. Far from the waist it spreads at the angle θ, so w(z) ≈ θ × z.
Real beams
Real lasers are not perfect Gaussians. The beam quality factor M² (ISO 11146) is 1 for an ideal TEM₀₀ beam and larger for real ones; replacing λ with M²λ in the formulas gives a shorter Rayleigh range and a faster spread for the same waist. A good helium-neon laser is close to 1, many diode lasers are well above it.
Units: wavelength in nanometers, waist and distance in millimeters. Results are in mm (Rayleigh range, radius) and milliradians (divergence). The trade-off is fixed by diffraction: a smaller waist means a faster-spreading beam.
| Distance from waist | Beam radius | Beam area |
|---|---|---|
| 0 | 1.00 × w₀ | 1× |
| 0.5 z_R | 1.12 × w₀ | 1.25× |
| 1 z_R | 1.41 × w₀ | 2× |
| 2 z_R | 2.24 × w₀ | 5× |
| 5 z_R | 5.10 × w₀ | 26× |
How to use
Enter the wavelength, waist radius and distance, leave M² blank for an ideal beam, and choose the output. The default is a 632.8 nm helium-neon beam with a 0.5 mm waist: z_R = π × 0.5² ÷ 0.0006328 = 1,241.15 mm; θ = 0.0006328 ÷ (π × 0.5) = 0.4 mrad; and at 1,000 mm the radius is 0.5 × √(1 + (1,000 ÷ 1,241.15)²) = 0.64 mm. A 532 nm beam with a 1 mm waist has z_R = 5,905 mm, so 500 mm from the waist it has barely grown (1.0036 mm). With M² = 1.5 the same 632.8 nm beam has a Rayleigh range of only 827.43 mm.
Frequently asked questions
What is the Rayleigh range?
The distance from the waist at which the beam radius has grown by √2 and its area has doubled. Twice the Rayleigh range is often called the depth of focus or confocal parameter.
How does the waist size affect divergence?
Divergence is inversely proportional to the waist: θ = M²λ ÷ (πw₀). Halving the waist doubles the spread, which is why beam expanders are used to send a beam a long way with little growth.
What does M² mean?
M² compares a real beam with a perfect Gaussian of the same waist. M² = 1 is ideal; M² = 2 diverges twice as fast and has half the Rayleigh range. It is measured from the second-moment beam widths defined in ISO 11146.
Is the waist a radius or a diameter?
A radius, measured to where the intensity falls to 1/e² (13.5%) of its peak. If your laser spec gives a beam diameter, divide by 2.
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Sources & references
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