Etendue Calculator
Calculate optical etendue from source area and solid angle or numerical aperture — the fundamental conserved quantity in optical systems.
Inputs
Full hemisphere = 2π ≈ 6.2832 sr
Air ≈ 1.0 · Glass ≈ 1.5 · Water ≈ 1.33 · Oil ≈ 1.515
Results
Enter values and click Calculate
Etendue (E = n²AΩ)
mm²·sr
cm²·sr
m²·sr
Half-angle θ
Solid angle Ω
Geometric etendue (AΩ)
Formula: E = n² × A × Ω
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Etendue is conserved — no passive optic can reduce it.
Common Presets
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Summary
Calculate optical etendue from source area and solid angle or numerical aperture — the fundamental conserved quantity in optical systems.
How it works
- Select input mode: Solid Angle or Numerical Aperture.
- Enter the source area and unit (mm², cm², or m²).
- Enter the solid angle in steradians, or the numerical aperture and refractive index.
- The calculator computes etendue using E = n² × A × Ω and displays it in multiple units.
- Use the results to compare with your detector or fiber etendue to assess coupling efficiency.
Use cases
- Check whether a fiber bundle can capture all light from an LED source.
- Determine the minimum detector size needed to collect all flux from a collimator.
- Compare source and system etendue to find the coupling efficiency bottleneck.
- Design illumination optics for projectors, microscopes, or laser systems.
- Verify throughput conservation when switching between immersion and air optics.
- Calculate the maximum brightness transfer possible through an optical train.
Frequently Asked Questions
Last updated: 2026-07-23 ·
Reviewed by Nham Vu