Beam Divergence & Diameter Calculator

Far-field geometric cone · solve for any one of four parameters

θ = arctan((D₂ − D₁) / 2L)

Inputs — any three of four

D₁ Initial diameter

D₂ Final diameter

L Distance between diameters

θ Divergence (half-angle)

Laser / optics presets

Cone geometry

TEM₀₀ Gaussian, constant divergence in a homogenous medium. Far-field / geometric cone model.

Outputs

Half-angle θ

—

θ = arctan((D₂−D₁)/2L)

Full angle 2θ

—

apex of full cone

Final diameter D₂

—

= D₁ + 2L·tan(θ)

Initial diameter D₁

—

= D₂ − 2L·tan(θ)

Distance L

—

= (D₂−D₁) / (2·tan θ)

Expansion ratio

—

D₂ / D₁

Virtual origin offset

—

back-projected apex behind D₁

Solid angle Ω

—

≈ π·θ² (small angle)

θ = arctan((D₂ − D₁) / (2·L)) · D(z) = D₁ + 2·z·tan(θ) · 2θ = full angle · Ω ≈ π·θ²
TEM₀₀ Gaussian beam, constant divergence, homogenous isotropic medium. Ref: Saleh & Teich, Fundamentals of Photonics, 2nd ed.