Beam Waist & Spot Size Calculator

Gaussian beam focusing through a thin lens — spot size, DOF, NA
2w₀ = 4 · M² · λ · f / (π · D)

Inputs

λ Wavelength
M² Beam quality factor
D Beam diameter at lens (1/e²)
f Focal length
Axial position (optional)
z Distance from focus (Δz = z − f)
evaluates D(z)
Δz 0 mm
Laser + Lens presets

Focused beam

collimated D lens f 2w₀ DOF z D
TEM₀₀ Gaussian beam · thin-lens, paraxial · waist coincides with focal plane.
Key results
Spot diameter 2w₀
—
= 4·M²·λ·f / (π·D)
Waist radius w₀
—
spot ÷ 2
Rayleigh range z_R
—
= π·w₀² / (M²·λ)
Depth of field (2·z_R)
—
tolerance for ≈√2 spot
Numerical aperture
—
NA ≈ D / (2·f)
f-number
—
f / D
Half-angle θ
—
= M²·λ / (π·w₀)
Diameter at z: D(z)
—
= 2w₀·√(1+(Δz/z_R)²)