Beam Divergence Calculator
Enter wavelength and beam waist. The Beam Divergence Calculator instantly computes full-angle divergence, Rayleigh range, and far-field behavior for Gaussian beams.
About the Beam Divergence Calculator
The Beam Divergence Calculator is a precise, scientifically accurate tool that computes Gaussian beam divergence using the fundamental formulas from laser physics and ISO 11146 standard. This Beam Divergence Calculator implements the exact expressions for half-angle divergence θ = λ/(π w₀), Rayleigh range z_R = π w₀²/λ, and beam radius evolution w(z). Proudly supported by Agri Care Hub.
Scientific Formulas
Full-angle divergence: 2θ
Rayleigh range: z_R = π w₀² / (λ M²)
Beam radius at z: w(z) = w₀ √(1 + (z/z_R)²)
Why This Calculator Is Essential
Beam divergence determines how fast a laser beam spreads — critical for: • Laser focusing and collimation • Optical system design • Fiber coupling efficiency • Long-distance propagation (LIDAR, free-space comm) • Material processing (spot size) • Medical laser safety Understanding divergence is essential for any laser application.
How to Use
- Enter wavelength λ in μm (e.g., 0.532 for green, 10.6 for CO₂).
- Enter beam waist w₀ (radius at 1/e²) in mm.
- Enter M² factor (1 for TEM₀₀, >1 for multimode).
- Enter distance z to see beam size evolution.
- Click “Calculate Beam Divergence”.
When Should You Use This Tool?
- Laser system design and alignment
- Optical engineering and photonics
- Fiber optics and coupling
- Free-space optical communication
- LIDAR and remote sensing
- Teaching Gaussian beam propagation
Scientific Foundation
Beam divergence for Gaussian beams is derived from the wave nature of light and diffraction. The fundamental limit θ = λ/(π w₀) is the diffraction limit. M² accounts for real beam quality. Full theory at Beam Divergence on Wikipedia and Siegman’s *Lasers* (1986).
Conclusion
The Beam Divergence Calculator brings professional laser beam propagation tools to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning Gaussian optics, a researcher designing laser systems, or an engineer optimizing beam delivery, this tool delivers precise results every time. For more optics tools, visit Agri Care Hub.