# Etendue calculator

Canonical: https://www.formlightoptics.com/tools/etendue
Markdown: https://www.formlightoptics.com/tools/etendue.md

Compare the etendue of a flat source with a fiber or an aperture. The coupling ratio is a geometric ceiling.

G = π n² A sin²(θ), with θ the half-angle from the normal.

For a fiber, G = π A NA², with NA the external numerical aperture in air.

Coupling = receiver etendue / source etendue, capped at 100%.

Passive optics cannot reduce etendue. They can reshape the beam, and they cannot make its etendue smaller.

Worked check: a 1 mm by 1 mm Lambertian source in air has etendue π mm² sr. A 1 mm core with NA 0.5 has etendue π²/16. The coupling ceiling is π/16.

Study: [LED-to-fiber coupling feasibility study](https://www.formlightoptics.com/portfolio/led-to-fiber-coupling-study).

Need more than an estimate? Get a fixed-fee design quote.

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