Laser Spot Size Calculator
When a Gaussian laser beam is focused by a lens, the minimum spot radius (beam waist) is w0 = 4 lambda f / (pi D), where lambda is the wavelength, f is the focal length of the focusing lens, and D is the 1/e^2 diameter of the input beam at the lens. A smaller spot is achieved with shorter wavelengths, longer input beam diameter, or shorter focal length. The depth of focus (two times the Rayleigh range) is 2 zR = 2 pi w0^2 / lambda. This calculator also shows the peak irradiance if you supply the beam power.
Laser spot size formulas
w0 = M2 x 4 lambda f / (pi D)
zR = pi w02 / (M2 lambda)
Ipeak = 2P / (pi w02)
Where lambda = wavelength, f = focal length, D = input beam diameter (all in same units). w0 is the 1/e2 spot radius at focus. Depth of focus = 2 zR.
Laser spot size applications
- Laser cutting and welding: smaller spot concentrates power for cutting thin metals. A 100 W CO2 laser focused to 50 um gives peak irradiance over 2.5 MW/cm^2.
- Laser lithography and photomask writing: UV lasers (248 nm, 193 nm) with large input beams and short focal lengths achieve sub-100 nm features.
- Laser scanning microscopy (confocal): tight focus with high-NA objective (f = 1-3 mm) at 488 nm gives sub-500 nm resolution.
- Optical data storage: DVD uses 650 nm; Blu-ray uses 405 nm with higher NA, giving smaller pit size and higher storage density.
Laser spot size: frequently asked questions
What is the focused laser spot size formula?
For a Gaussian beam focused by a lens of focal length f with an input beam diameter D, the focused waist radius is w0 = 2 lambda f / (pi w_in), where w_in = D/2 is the input beam radius at the lens. In terms of input beam diameter D: w0 = 4 lambda f / (pi D). This is the 1/e^2 intensity radius at the focal point.
What does the 1/e^2 radius mean?
For a Gaussian beam, the 1/e^2 radius (w) is the distance from the beam axis where intensity falls to 1/e^2 (about 13.5%) of the peak. The full 1/e^2 diameter is 2w. This convention is standard in laser optics. The spot contains 86.5% of the total beam power within the 1/e^2 radius circle.
How does beam quality (M^2) affect spot size?
A real laser beam with beam quality factor M^2 > 1 produces a larger focused spot: w0_real = M^2 x (4 lambda f / (pi D)). A perfect Gaussian has M^2 = 1. Multimode lasers may have M^2 of 10 to 100 or more, resulting in correspondingly larger spots.
How is laser irradiance (intensity) related to spot size?
Peak irradiance at the focused spot is I_peak = 2P / (pi w0^2), where P is the beam power in watts. A smaller spot concentrates the same power into a smaller area, increasing irradiance. Halving the spot size increases peak irradiance by a factor of 4.
What focal length do I need to achieve a given spot size?
Rearranging: f = pi w0 D / (4 lambda M^2). For a 10 um spot at 1064 nm with M^2 = 1 and D = 10 mm input beam: f = pi x 10e-6 x 10e-3 / (4 x 1064e-9 x 1) = approximately 73.9 mm. Use a shorter focal length lens to achieve smaller spots.
Official sources
- Optica (formerly OSA) standards on laser beam characterization. optica.org.
- NIST, Physical Measurement Laboratory. physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.