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Gaussian Beams Calculator

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Mathematically model beam propagation of Gaussian beam using simple geometric parameters. Calculator uses first order approximations and assumes TEM00 mode to determine beam spot size in free space applications. Please note that results will vary based on beam quality and application conditions.

Enter your Information

Axial Distance, z (mm):

Beam Waist, ω0 (mm):

Wavelength, λ (μm):


Half Beam Diameter, ω(z) (mm): --        

Radius of Curvature, R(z) (mm): --        

Rayleigh Range, ZR (mm): --        

Rayleigh Half Diameter, ωR(b/2): --        

Half Angle Divergence, θ (mrad): --        

Note: Results greater than 1,000,000 are rounded to infinity.
Gaussian Beam Calculator

Equations and Corresponding Legend

$$ z_R = \frac{\pi \omega_0 ^2}{\lambda} $$
$$ \omega \! \left( z \right) = \omega_0 \sqrt{1 + \left( \frac{z}{z_R} \right) ^2} $$
$$ \omega_R \! \left( \tfrac{b}{2} \right) = \sqrt{2} \, \omega_0 $$
$$ z_R = \frac{b}{2} $$
$$ R \! \left( z \right) = z \left[ 1 + \left( \frac{z_R}{z} \right)^2 \right] $$
$$ \theta = \frac{\lambda}{\pi \, \omega_0} $$
λ Wavelength
zR Rayleigh Range
z Axial Distance
ω(z) Half Beam Diameter
ω0 Beam Waist
b Confocal Parameter
ΖR Rayleigh Half Diameter
R(z) Radius of Curvature
θ Half Angle Divergence

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