Free · Physics models
Gaussian Laser Focus Diameter and Rayleigh Range
Estimate a paraxial Gaussian beam focus diameter, Rayleigh range and confocal depth from a collimated input beam.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
spot = 0.027094538 mm; rayran = 0.54189075 mm; depth = 1.0837815 mm.
d₀ = 4 M² λ f/(π D); zR = π d₀²/(4 M² λ); depth = 2 zR.
Worked example
Enter these known values and leave the other values blank.
- Wavelength (λ)
- 1064 nm
- Diameter at the lens (d)
- 5 mm
- Focal length (f)
- 100 mm
- Beam quality factor (M²)
- 1
- Beam spot size (S)
- 0.027095 mm
- Depth of focus
- 1.0838 mm
Assumptions and limitations
- Estimate a paraxial Gaussian beam focus diameter, Rayleigh range and confocal depth from a collimated input beam.
- Input and focused spot are full 1/e² intensity diameters, not radii or FWHM. The beam-factor control is M² and must be at least one.
- Assume a thin ideal focusing optic, positive wavelength, focal length and beam diameter. Aberration, clipping and high numerical aperture effects are excluded.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
Common questions
Why is the spot a diameter?
The coefficient of four uses full input and focused 1/e² intensity diameters. Radius-based equations use a different coefficient.
What does depth mean here?
It is twice the Rayleigh range, the Gaussian confocal parameter.
References
Estimate a paraxial Gaussian beam focus diameter, Rayleigh range and confocal depth from a collimated input beam. Input and focused spot are full 1/e² intensity diameters, not radii or FWHM. The beam-factor control is M² and must be at least one. Assume a thin ideal focusing optic, positive wavelength, focal length and beam diameter. Aberration, clipping and high numerical aperture effects are excluded.