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Gaussian Beam Waist, Rayleigh Range & Divergence Calculator

Easily calculate and compute gaussian beam waist, rayleigh range & divergence calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
2,249.2 μm

Beam Radius at Distance z (w(z))

Beam Radius at Distance z (w(z))

2,249.2 μm

Rayleigh Range Meters

0.168

Divergence Half Angle Mrad

1.49

Confocal Parameter Meters

0.336

Far Field Criterion Met

FAR FIELD REGIME (Linear Angular Expansion)

2,249.2 — μm

Calculation Breakdown

  1. Applied FormulaModels fundamental TEM00 Gaussian laser beam spatial profile expansion, computing Rayleigh range zR, confocal parameter b, half-angle divergence theta, and beam spot radius at distance z.w(z) = w_0 \sqrt{1 + \left(\frac{z}{z_R}\right)^2}, \quad z_R = \frac{\pi w_0^2}{\lambda}, \quad \theta_{\text{div}} = \frac{\lambda}{\pi w_0}

Gaussian Beam Propagation Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.05621.1k1.7k2.2kBeam Radius at Distance z (w(z))

What Is the Gaussian Beam Waist, Rayleigh Range & Divergence Calculator?

This tool computes gaussian beam waist, rayleigh range & divergence calculator with high precision arithmetic.

How Does the Gaussian Beam Waist, Rayleigh Range & Divergence Calculator Work?

Models fundamental TEM00 Gaussian laser beam spatial profile expansion, computing Rayleigh range zR, confocal parameter b, half-angle divergence theta, and beam spot radius at distance z.

Gaussian Beam Waist, Rayleigh Range & Divergence Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

w(z)=w01+(zzR)2,zR=πw02λ,θdiv=λπw0w(z) = w_0 \sqrt{1 + \left(\frac{z}{z_R}\right)^2}, \quad z_R = \frac{\pi w_0^2}{\lambda}, \quad \theta_{\text{div}} = \frac{\lambda}{\pi w_0}

Models fundamental TEM00 Gaussian laser beam spatial profile expansion, computing Rayleigh range zR, confocal parameter b, half-angle divergence theta, and beam spot radius at distance z.

How to Use the Gaussian Beam Waist, Rayleigh Range & Divergence Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Gaussian Beam Waist, Rayleigh Range & Divergence Calculator Example

Input Values:

beamWaistRadiusMicrons:250
laserWavelengthNm:1064
propagationDistanceMeters:1.5
beamQualityFactorM2:1.1
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required μm.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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