Laser Spot Size Calculator (focused Gaussian beam waist, Rayleigh range)

Understanding the laser spot size calculator — concept and principle

This calculator finds the diameter of the focused spot when a collimated laser beam passes through a lens, together with the Rayleigh range, depth of focus, working f-number, the diffraction-limited spot and the peak intensity per watt. Laser cutting, marking, microscopy and fibre coupling all depend on these numbers.

A wider beam or shorter lens gives a smaller spot, but the depth of focus shrinks with it.

How it is calculated

Spot diameter 2w₀ = 4 M² λ f ÷ (π D)

Rayleigh range z_R = π w₀² ÷ (M² λ); depth of focus = 2 z_R

Working f-number = f ÷ D

Peak intensity per watt = 2 ÷ (π w₀²)

λ in nm, D (1/e² beam diameter at the lens) in mm, f in mm.

The principle

A lens cannot focus light to a perfect point because of diffraction. For a Gaussian beam the smallest waist is set by the wavelength and by how steeply the lens bends the beam, which is the ratio f/D. Longer wavelengths, longer focal lengths and narrower beams all give bigger spots; that is why expanding a beam before the lens makes the spot smaller. Around the focus the beam stays nearly as small as w₀ over the Rayleigh range, within which the radius grows to √2 w₀. Tight focusing therefore buys a small spot at the cost of a short depth of focus.

Worked example

Default inputs: λ = 1,064 nm, D = 6 mm, f = 100 mm, M² = 1.1.

2w₀ = 4 × 1.1 × 1,064 × 10⁻⁹ × 0.1 ÷ (π × 0.006) = 24.84 µm; radius 12.42 µm.
z_R = π × (12.42 × 10⁻⁶)² ÷ (1.1 × 1,064 × 10⁻⁹) = 0.4139 mm; depth of focus 0.8279 mm.
f-number = 100 ÷ 6 = 16.67; diffraction-limited spot (M² = 1) = 22.58 µm.
Peak intensity = 2 ÷ (π × (12.42 × 10⁻⁴ cm)²) = 412.8 kW/cm² per watt.

Each point is the calculator re-run with only “Beam diameter at the lens (mm, 1/e²)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Beam diameter at the lens (mm, 1/e²)	Focused spot diameter 2w₀ (µm)
1.5	99.35
3	49.67
4.5	33.12
6	24.84
7.5	19.87
9	16.56
12	12.42

How to read the result

Multiply the peak intensity by your laser power to compare with a material's processing threshold. If you need a smaller spot, use a shorter focal length or a wider beam; if you need more tolerance in focus position, accept a larger spot. Real spots are larger if the lens has aberrations or is overfilled.

Common mistakes

Using the beam's FWHM instead of its 1/e² diameter.
Overfilling the lens aperture, which clips the beam and adds rings.
Ignoring M² for multimode lasers.
Using the formula for very tight focusing (high numerical aperture), where it becomes less accurate.

Keep in mind: Focused laser beams can burn skin, ignite materials and damage eyes instantly. Use enclosures and the protective eyewear required for your laser.

Frequently asked questions

How do I get a smaller spot?

Use a shorter focal length or expand the beam before the lens.

What is depth of focus?

Twice the Rayleigh range, the length over which the spot stays within √2 of its smallest radius.

Why does a 1,064 nm laser give a bigger spot than a 532 nm one?

The spot size is proportional to the wavelength.

What does M² do to the spot?

It multiplies the spot diameter and shortens the Rayleigh range for a given spot.

Sources: Melles Griot Optics Guide, Chapter 2 "Gaussian Beam Optics" (2005) · R. Paschotta, RP Photonics Encyclopedia, "M² factor"

Checked 9 Nov 2026. Melles Griot Optics Guide, Chapter 2 “Gaussian Beam Optics” (2005), as compiled in Michigan State University PHY 431 notes: focal spot 2w₀ = (4λ/π)(f/D), Rayleigh range z_R = πw₀²/λ, depth of focus = 2z_R, irradiance I(r) = I₀ exp(−2r²/w²). Real beams: replace λ by M²λ (RP Photonics Encyclopedia, “M² factor”).

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