ONE FORMULA, ONE ANSWER
Gaussian Beam Radius Calculator
Calculate the radius of an ideal Gaussian beam at a distance from its waist. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Intensity 1/e² beam radius w(z)
Enter values and select Calculate.
w(z) = w₀√[1+(z/z_R)²], z_R=πnw₀²/λ₀
Assumptions
Required: λ₀,w₀,n>0 and signed z. The radius is where intensity falls to 1/e² of its on-axis value. Assume a fundamental TEM₀₀ mode with M²=1 in a homogeneous isotropic linear lossless medium. Excluded: lenses, apertures and nonlinear propagation. The app enforces the paraxial condition λ₀/(πnw₀)≤0.1 rad. Enter the vacuum wavelength; the refractive index is applied internally.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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