Laser Beam Divergence Calculator

Laser Beam Divergence

Beam divergence measures how quickly a laser beam spreads as it propagates. It is critical for optical system design, safety calculations, and determining spot size at a target distance.

Formulas

Geometric divergence from beam diameter and propagation distance:

$$\theta = 2 \arctan\left(\frac{d}{2z}\right)$$

Gaussian beam approximation from wavelength and waist radius:

$$\theta \approx \frac{\lambda}{\pi w_0}$$

Results are typically expressed in milliradians (mrad). Full angle divergence is used throughout.

Practical Notes

Use the geometric method when you know the beam diameter at a measured distance. Use the Gaussian method for diffraction-limited beams where wavelength and waist radius are known.

Frequently Asked Questions

What is the difference between full and half angle divergence?

Full angle is the total spread from edge to edge. Half angle is measured from the beam axis to the edge. This calculator uses full angle.

When should I use the Gaussian formula?

Use it for TEM₀₀ Gaussian beams where the waist radius and wavelength define the diffraction-limited divergence.

What units are used for wavelength?

Enter wavelength in nanometers (nm). Common HeNe lasers use 632.8 nm.

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Laser Beam Divergence Calculator