Gaussian Beam Waist Calculator

Calculator

Choose a solving path, enter the known beam data, and submit. The result appears above this form and directly below the header section.

Calculation mode

Wavelength (nm)

Beam quality M²

Half-angle divergence θ (mrad)

Rayleigh range zR (mm)

Lens focal length f (mm)

Input beam diameter D (mm)

Laser power (mW)

Observation distance z (mm)

Graph extent on each side of waist (mm)

Example data table

This sample table shows typical optical inputs and approximate outputs produced by the calculator.

Mode	Inputs	Approximate waist radius	Approximate Rayleigh range	Approximate full divergence
Divergence	632.8 nm, M² 1.0, θ = 0.50 mrad	402.8530 µm	805.7060 mm	1.000000 mrad
Rayleigh range	1064 nm, M² 1.2, zR = 35 mm	119.2671 µm	35.0000 mm	6.815261 mrad
Lens focus	532 nm, M² 1.1, f = 100 mm, D = 2.5 mm	14.9020 µm	1.1922 mm	25.000000 mrad

Formula used

The calculator follows standard Gaussian beam relations with the 1/e² radius definition.

w0 = (M²λ) / (πθ) for solving waist from far-field half-angle divergence.
w0 = √(M²λzR / π) for solving waist from Rayleigh range.
w0 ≈ (2M²λf) / (πD) for a collimated beam focused by a thin lens.
zR = πw0² / (M²λ) for Rayleigh range.
w(z) = w0√(1 + (z/zR)²) for beam radius at distance z.
θfull = 2M²λ / (πw0) for full-angle divergence.
I0 ≈ 2P / (πw0²) for approximate on-axis peak intensity of a TEM₀₀ beam.
R(z) = z[1 + (zR/z)²] for wavefront curvature away from the waist.

How to use this calculator

Select the solving mode that matches the data you already know.
Enter wavelength, beam quality M², and any required mode-specific inputs.
Optionally add power to estimate peak intensity at the waist.
Set an observation distance to evaluate beam radius away from focus.
Choose a graph extent to visualize propagation on both sides of the waist.
Click the calculate button to show the result block above the form.
Review the table, graph, and derived metrics for design or alignment work.
Use the CSV or PDF buttons to save the calculated summary.

Frequently asked questions

1) What is Gaussian beam waist?

The beam waist is the location where a Gaussian beam reaches its minimum 1/e² radius. That radius is written as w0 and controls divergence, Rayleigh range, spot area, and focusing behavior.

2) Why does the calculator ask for M²?

M² adjusts ideal Gaussian formulas for real beams. A perfect TEM00 beam has M² = 1. Higher values mean poorer focusability, larger beam parameter product, and stronger divergence for the same waist size.

3) Is divergence entered as half-angle or full-angle?

The divergence input in this page is the far-field half-angle, measured from the optical axis to the 1/e² beam envelope. The result table reports both half-angle and full-angle divergence values.

4) What does Rayleigh range tell me?

Rayleigh range is the distance from the waist to the point where the beam radius grows by √2. It describes how quickly a beam spreads and defines the confocal parameter as 2zR.

5) When should I use the lens mode?

Use lens mode when a collimated beam is focused by a lens and you know wavelength, focal length, input beam diameter, and beam quality. It estimates the diffraction-limited waist near focus.

6) Does the power input change the waist result?

No. Power does not change the geometric waist calculation. It is only used to estimate the approximate on-axis peak intensity at the waist, assuming a Gaussian beam profile.

7) What is beam parameter product?

Beam parameter product combines waist radius and half-angle divergence into one quality metric. Lower values indicate tighter focusing and better spatial quality, while real beams increase with larger M².

8) Are the results suitable for laboratory design?

Yes, for quick engineering estimates and educational optics work. Final laboratory design should still confirm conventions, actual beam profiles, lens aberrations, truncation effects, and manufacturer data.