# LED beam angle calculator

Canonical: https://www.formlightoptics.com/tools/led-beam-angle
Markdown: https://www.formlightoptics.com/tools/led-beam-angle.md

Relate a round spot on a flat target to the full angle of the beam, or run the same geometry in reverse.

θ = 2 arctan(D / (2 L)), with D the spot diameter and L the throw in the same units.

D = 2 L tan(θ / 2).

Beam angle is the full width at half the peak intensity (FWHM). Field angle is the full width at 10% of the peak. The geometry uses the contour you measured. It does not convert one into the other.

On-axis illuminance from intensity is E = I / d², with I in candela and d in meters. The cosine factor is 1 on axis.

From flux, I = flux / (2π (1 - cos(θ / 2))), then E = I / d². That uniform cone overstates on-axis lux when θ is an FWHM beam angle.

Worked check: a 1 m spot at a 1 m throw has full angle 2 arctan(0.5). 1000 cd at 2 m is 250 lux.

Portfolio: [Beam-angle lens family for a clustered LED downlight](https://www.formlightoptics.com/portfolio/clustered-led-downlight-beam-angle-lenses).

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