Laser Spot Size Calculator — Gaussian Beam Focus
Enter the laser wavelength, input beam radius at the lens, focal length and beam quality factor M² to get the focused spot radius, Rayleigh range and depth of focus for a Gaussian beam.
nm
mm
mm
1/e² intensity radius at the focal plane
- 1
Wavelength in mm
1,064 nm × 10⁻⁶ = 0.001064Convert nm to mm so all lengths share the same unit. - 2
Spot radius w₀ (mm)
M² × λ × f ÷ (π × w) = 1 × 0.001064 × 100 ÷ (π × 5) = 0.00677 - 3
Focused spot radius (µm)
0.00677 × 1000 = 6.774
How does this calculator work?
A Gaussian beam focused by a thin lens forms a spot of radius w₀ = M²·λ·f/(π·w), where λ is wavelength, f is focal length, w is input beam radius and M² is beam quality. The Rayleigh range z_R = π·w₀²/(M²·λ) sets the depth of focus (2·z_R). Smaller spot = shorter depth of focus.
Formula
How this is calculated
When a collimated Gaussian laser beam of wavelength λ and 1/e² radius w passes through a thin lens of focal length f, it is focused to a minimum waist radius w₀ = M²·λ·f/(π·w). This formula assumes the input beam fills the lens aperture and treats the lens as ideal (no aberrations). The M² factor (beam quality factor, always ≥ 1) scales the spot linearly: a diffraction-limited TEM₀₀ beam has M² = 1; real beams are larger by the factor M².
The Rayleigh range z_R = π·w₀²/(M²·λ) is the distance from the focus at which the beam radius has grown by √2 (the cross-sectional area has doubled). It characterises how quickly the beam diverges: a tighter focus has a shorter Rayleigh range, meaning the spot stays small only over a limited axial distance. The depth of focus (DOF = 2·z_R) is the useful working distance around the focus.
The profile plot shows the beam width w(z) = w₀·√(1+(z/z_R)²) on either side of the focus. Assumptions: thin lens, paraxial (small angle) approximation, Gaussian (TEM₀₀ or M²-scaled) beam, no aberrations. For very tight foci (spot size approaching wavelength) or high-NA focusing, the paraxial model becomes inaccurate.
Frequently asked questions
Decrease wavelength, increase focal length (but that widens the Rayleigh range proportionally) — or, most effectively, expand the input beam radius w before focusing (the spot scales as 1/w). A larger beam at the lens gives a tighter focus, which is why telescopes are placed before focusing lenses in many laser systems.
M² (M-squared, beam quality factor) measures how close a beam is to the diffraction limit. M² = 1 is a perfect Gaussian; typical single-mode fibre lasers give M² ≈ 1.05–1.2; diode bars and multimode fibres can reach M² = 10–100. The focused spot radius scales directly with M², so a higher M² means a larger, less intense focus.
The depth of focus (2·z_R) scales as w₀² and is inversely proportional to the spot area — Heisenberg-like uncertainty between transverse confinement and longitudinal divergence. Halving the spot radius reduces z_R by four times. This trade-off is fundamental and cannot be beaten without near-field techniques.
Also known as
TG we-Calculate Editorial Team. (2026). Laser Spot Size Calculator — Gaussian Beam Focus [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/laser-spot-size-calculator
TG we-Calculate Editorial Team. "Laser Spot Size Calculator — Gaussian Beam Focus." TG we-Calculate. 2026. https://we-calculate.com/calculator/laser-spot-size-calculator.
TG we-Calculate Editorial Team, "Laser Spot Size Calculator — Gaussian Beam Focus," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/laser-spot-size-calculator
@misc{wecalculate_laser_spot_size_calculator, title = {Laser Spot Size Calculator — Gaussian Beam Focus}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/laser-spot-size-calculator}}, year = {2026}, note = {TG we-Calculate} }
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