Laser Beam Divergence Calculator
Calculate laser beam divergence angle and beam expansion over distance for optical applications
Calculate Laser Beam Divergence
Find Divergence
Calculate divergence angle from beam measurements
Find Final Diameter
Calculate beam diameter at given distance
Beam diameter at the initial measurement point
Beam diameter at the final measurement point
Distance between initial and final measurement points
Laser Beam Divergence Results
Divergence Angle
Beam Expansion
Formula used: Θ = 2 × arctan((Df - Di) / (2 × l))
Measurement conditions: Far-field approximation at 1/e² intensity points
Theoretical minimum: 0.201 mrad (diffraction limit)
Beam Quality Analysis
Example Calculation
Typical Laser Pointer
Initial diameter: 4 mm (at laser aperture)
Final diameter: 7.5 mm (at 10 meters)
Distance: 10 m
Calculation: Θ = 2 × arctan((7.5 - 4)/(2 × 10,000)) = 0.35 mrad
Beam Expansion Prediction
• At 100 m: diameter ≈ 39 mm (3.9 cm)
• At 1 km: diameter ≈ 354 mm (35.4 cm)
• Expansion rate: 0.175 mm per meter of propagation
Typical Laser Divergences
Laser Divergence Facts
Measured at 1/e² intensity points (86% of total power)
Gaussian beams have minimum possible divergence
Larger initial diameter = smaller divergence
Diffraction limits minimum achievable divergence
Far-field approximation needed for accurate measurement
Understanding Laser Beam Divergence
What is Beam Divergence?
Laser beam divergence measures how much a laser beam spreads as it propagates through space. Even the most collimated laser beams expand over distance due to fundamental physics principles, particularly diffraction effects at the beam aperture.
Why Does Divergence Matter?
- •Determines beam spot size at target distance
- •Affects power density and intensity distribution
- •Critical for laser rangefinding and targeting
- •Important for optical communication systems
Mathematical Formula
Θ = 2 × arctan((Df - Di) / (2 × l))
- Θ: Full divergence angle (radians)
- Df: Final beam diameter
- Di: Initial beam diameter
- l: Distance between measurements
Diffraction Limit: For Gaussian beams, minimum divergence is θ = M² × λ / (π × w₀), where λ is wavelength and w₀ is beam waist radius.
Applications and Considerations
Laser Ranging
LIDAR and rangefinder systems require precise divergence control to maintain accuracy over long distances while avoiding excessive beam spread.
Material Processing
Laser cutting, welding, and engraving require controlled beam divergence to maintain consistent power density and processing quality.
Optical Communication
Free-space optical links depend on minimal beam divergence to maximize signal strength at the receiver over atmospheric paths.