Laser Beam Divergence Calculator
Calculate the divergence angle of a Gaussian laser beam
Common values: 532 nm (green), 632.8 nm (HeNe red), 1064 nm (Nd:YAG)
The radius of the beam at its narrowest point (waist)
How to Use This Calculator
Enter the Wavelength
Input the wavelength of the laser in meters. Common laser wavelengths: 532 nm (green) = 0.000000532 m, 632.8 nm (HeNe red) = 0.0000006328 m, 1064 nm (Nd:YAG) = 0.000001064 m.
Enter the Beam Waist
Input the beam waist radius (w₀) in meters. This is the radius of the laser beam at its narrowest point, typically at the laser output or focus. Common values range from 10 μm to 1 mm.
Calculate
Click the "Calculate Beam Divergence" button to get the half-angle divergence in milliradians, radians, and degrees.
Formula
θ = λ / (π × w₀)
Where:
- θ = Beam divergence half-angle (in radians)
- λ = Wavelength (in meters)
- w₀ = Beam waist radius (in meters)
- π = Pi (approximately 3.14159)
Note: This formula applies to Gaussian beams in the far field. The result is the half-angle divergence, so the full angular spread is 2θ.
Example Calculation:
For a 532 nm laser with 100 μm beam waist:
λ = 0.000000532 m (532 nm)
w₀ = 0.0001 m (100 μm)
θ = 0.000000532 / (π × 0.0001)
θ = 0.000000532 / 0.000314 = 0.001694 radians
θ = 1.694 mrad (milliradians)
About Laser Beam Divergence Calculator
Laser beam divergence is a measure of how much a laser beam spreads out as it propagates. Unlike ideal parallel light, real laser beams diverge due to diffraction, which is fundamentally related to the beam's wavelength and minimum beam size (waist). This calculator uses the Gaussian beam model to determine the divergence angle, which is crucial for understanding laser propagation, designing optical systems, and calculating beam sizes at various distances.
When to Use This Calculator
- Laser System Design: Calculate divergence for laser pointer, cutting, or measurement systems
- Optical Design: Understand beam propagation in optical systems and determine beam sizes at target distances
- Research: Analyze laser beam characteristics for scientific experiments
- Quality Control: Verify laser beam specifications and performance
- Educational Purposes: Learn about Gaussian beam optics and diffraction limits
Why Use Our Calculator?
- ✅ Instant Results: Get accurate divergence calculations immediately
- ✅ Easy to Use: Simple interface requiring only wavelength and beam waist
- ✅ Multiple Units: Results displayed in milliradians, radians, and degrees
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works perfectly on all devices
Common Applications
Laser Pointers and Alignment: Understanding beam divergence helps predict how large a laser spot will be at a given distance. A laser pointer with 1 mrad divergence will produce a 1 mm spot at 1 meter, but a 10 cm spot at 100 meters.
Laser Cutting and Material Processing: Beam divergence affects the spot size and power density at the workpiece. For precise cutting, engineers need to know the beam size at the target to calculate power density and cutting parameters.
Optical Communications: In free-space optical communications, beam divergence determines how much power is received at the detector and how much alignment precision is needed between transmitter and receiver.
Tips for Best Results
- Use consistent units (meters for both wavelength and beam waist)
- Beam waist is typically measured at the 1/e² intensity point
- Smaller beam waists produce larger divergence (fundamental diffraction limit)
- Shorter wavelengths produce smaller divergence for the same beam waist
- For focused beams, the waist is at the focus point
- Remember that divergence is the half-angle; full beam spread is 2θ
Frequently Asked Questions
Why do laser beams diverge?
Laser beams diverge due to diffraction, which is a fundamental wave property. Even a perfectly collimated beam will diverge because of the uncertainty principle: a beam with finite width cannot have zero divergence. The divergence is inversely proportional to the beam waist—smaller beams diverge more.
What's the difference between half-angle and full-angle divergence?
Half-angle divergence (θ) is the angle from the beam axis to the edge. Full-angle divergence is 2θ, representing the total angular spread. The calculator shows half-angle, which is the standard convention in optics.
Can I reduce beam divergence?
You can reduce divergence by using a larger beam waist (bigger beam at the focus) or by using a telescope to expand and recollimate the beam. However, the fundamental limit is given by the formula—smaller beams always diverge more due to diffraction.
How does this relate to beam quality (M²)?
Real lasers have M² > 1 (higher than ideal Gaussian beams). The actual divergence is M² times the theoretical divergence. This calculator gives the theoretical (ideal) divergence; multiply by M² for real laser beams.
What's a typical divergence value?
Typical laser pointers have divergences of 1-2 mrad. High-quality laser systems can achieve 0.1-0.5 mrad. Very tight beams (like those from optical fibers) can have divergences of 10-100 mrad. The exact value depends on wavelength and beam waist.