Gaussian Beam Waist Calculator
Enter wavelength and beam waist to compute Rayleigh range, far-field divergence angle, and beam radius at any distance along the optical axis.
Beam Parameters
Visible: 380–700 nm. Common: 405, 532, 633, 780, 1064 nm.
Minimum 1/e² intensity radius at the focal plane.
Distance from the beam waist along the optical axis.
Results
Rayleigh Range zR
—
Distance where beam area doubles
Half-Angle Divergence θ
—
Far-field divergence half-angle
Beam Radius at z
—
1/e² intensity radius at distance z
Beam Diameter at z
—
Full 1/e² beam diameter at z
Confocal Parameter b
—
b = 2·zR (depth of focus)
Diffraction Limit (BPP)
—
Beam parameter product w0·θ = λ/π
Beam Radius Profile
Formulas Used
zR = π·w0² / λ — Rayleigh range
θ = λ / (π·w0) — far-field half-angle divergence
w(z) = w0 · √(1 + (z/zR)²) — beam radius at distance z
b = 2·zR — confocal parameter (depth of focus)
Summary
Enter wavelength and beam waist to compute Rayleigh range, far-field divergence angle, and beam radius at any distance along the optical axis.
How it works
- Enter the laser wavelength in nanometers.
- Enter the beam waist radius w0 — the minimum 1/e² intensity radius.
- Optionally set a propagation distance z to find the beam radius at that point.
- The calculator applies the paraxial Gaussian beam equations from scalar diffraction theory.
- Results update instantly as you type.
Use cases
- Design laser focusing optics and estimate the depth of focus.
- Calculate spot size at a detector placed a known distance from the waist.
- Determine collimation quality of a diode laser beam.
- Estimate far-field divergence for beam-steering or free-space communication links.
- Verify that a beam fits within an optical aperture at a given distance.
- Teach Gaussian optics in a physics or photonics course.