Estimate divergence angles to check alignment and focus. Compare theoretical limits with measured spot growth. Export your setup data, results, and notes for reports.
This calculator supports three common beam divergence models. It reports both the half-angle and the full-angle divergence.
| Method | Inputs | Half-angle (deg) | Full-angle (mrad) |
|---|---|---|---|
| Gaussian | λ=632.8 nm, w0=0.5 mm, M²=1 | 0.023074 | 0.8056 |
| Aperture | λ=532 nm, D=2.0 mm, k=1.22 | 0.018640 | 0.6508 |
| Two-point | w1=1.0 mm at z1=0 m; w2=3.0 mm at z2=1 m | 0.114592 | 4.0000 |
Examples are illustrative and depend on radius definitions and measurement conditions.
Beam divergence is the angular spread of a beam as it propagates. During alignment checks, in the far field it links radius growth to distance. Lower divergence supports tighter focusing and long-range delivery; higher divergence can signal clipping, aberrations, or poor mode quality.
Some references define divergence as a half-angle from the axis to the beam edge, while others quote the full cone angle. This calculator reports both. When comparing datasheets or lab results, confirm the convention and the beamwidth definition before drawing conclusions.
Milliradians are common because divergences are usually small. A few tenths of a milliradian is typical for near diffraction-limited sources, while several milliradians can occur for multimode diodes or clipped beams. Always interpret divergence alongside wavelength and beam size. For telecom or free-space links, log divergence per axis.
If you know the waist radius, the Gaussian model relates divergence to wavelength and beam quality. Smaller waists and longer wavelengths increase divergence. M² scales the ideal limit to match real beams affected by aberrations or higher-order modes, giving a practical prediction for system budgets.
When an aperture limits the beam, diffraction sets a floor on divergence. For a circular stop, k≈1.22 corresponds to the first Airy minimum. If you use a different width definition such as FWHM, an equivalent k may change, so keep definitions consistent across comparisons.
Two-point measurements estimate divergence from radius change over distance. Choose points far enough apart to beat noise, and preferably in the far field where growth is close to linear. Use the same radius definition at both points and avoid saturation or blooming in sensors.
M² summarizes how closely a beam behaves like an ideal Gaussian and predicts both divergence and best-focus size. It does not by itself capture astigmatism, ellipticity, or pointing jitter. For higher confidence, measure divergence in orthogonal axes and track stability over time.
To reduce divergence, prevent clipping, keep optics clean, and collimate carefully. Beam expansion increases diameter and lowers downstream diffraction-limited divergence. For lasers, stable operating current and temperature help maintain mode quality. Recheck divergence after mechanical changes or transport, and note the measurement date.
Most optical divergences are small. Milliradians keep numbers readable and map well to geometry: 1 mrad corresponds to about 1 mm radius growth per meter in the far field, under small-angle assumptions.
Report the convention required by your standard or customer. If uncertain, include both half-angle and full-angle values and clearly label them. That prevents confusion when comparing to datasheets or acceptance criteria.
M² quantifies how much a real beam departs from an ideal Gaussian. Values above 1 indicate additional spatial modes or aberrations. Higher M² increases divergence and limits the minimum focused spot size achievable with perfect optics.
Use k≈1.22 for the first Airy minimum of a circular aperture. If your beamwidth definition is FWHM or 1/e² radius, an equivalent factor may differ. Keep k consistent with your measurement definition.
Choose separation large enough that the radius change is clearly above measurement noise. If possible, work in the far field where growth is nearly linear. Avoid placing both points near a waist where curvature can bias results.
As a magnitude, divergence is nonnegative. A decreasing radius between two points usually means you crossed a waist or used inconsistent radius definitions. Swap point order or use absolute differences, then interpret results with beam geometry in mind.
Use a consistent definition throughout: commonly the 1/e² intensity radius for lasers, or another agreed beamwidth such as FWHM. Mixing definitions across measurements will distort the inferred divergence and hinder comparisons.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.