Gaussian Beam Radius Calculator
Calculate ideal Gaussian beam radius, Rayleigh length and divergence from the waist and wavelength.
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Result
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Calculation steps
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How to calculate
Use an ideal paraxial Gaussian beam with M²=1 and wavelength in the propagation medium.
zR=πw₀²/λ; w(z)=w₀√[1+(z/zR)²]; far-field half angle=λ/(πw₀)
Worked example
At the waist, radius isw0. At one Rayleigh length, radius is√2w0 and area doubles. For0.5mm waist and632.8nm wavelength, zR≈1.24114754m.
Assumptions and input details
Waist is the 1/e² intensity radius, not diameter or FWHM. Wavelength must already refer to the propagation medium; refractive index is not assumed. This ideal M²=1 model requires computed paraxial half-angle divergence≤0.1rad. Signed distances on either side of the waist give equal radii at equal magnitude. No lens system, clipping, astigmatism, measured beam quality or laser safety assessment is performed.
References: University of Colorado: Gaussian beams laboratory
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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