Beam Angle Formula

The beam angle and the distance to the surface set how wide the lit circle is. The beam diameter grows with the tangent of half the beam angle.

D = 2 × d × tan(θ ÷ 2)

What the terms mean

Symbol Meaning
D Beam diameter at the surface
d Distance to the surface
θ Full beam angle, in degrees

Worked example

A 30° beam at 3 m gives D = 2 × 3 × tan(15°) = about 1.6 m across.

Beam vs field angle. Beam angle is measured to 50% of peak intensity; field angle (to 10%) is wider and defines the visible spill. Manufacturers list both.

See the Beam Angle Comparison and CBCP Comparison.

Beam angle and spot size

The beam angle and the throw distance together set how wide the lit circle is. The geometry is straightforward: the beam diameter grows with the tangent of half the beam angle — diameter ≈ 2 × distance × tan(beam angle ÷ 2). So a 30° beam at 3 metres lights a circle about 1.6 metres across, while a 60° beam at the same distance covers roughly 3.5 metres.

Narrow beams (under ~25°) concentrate light for accent and long throws; wide beams (40°+) cover area for general and wall lighting. Remember the trade-off: for a fixed lumen output, a narrower beam gives a brighter, smaller pool (higher candela) and a wider beam a dimmer, larger one. Use the beam-angle and distance relationship to plan fixture spacing so the pools overlap for even coverage.

Scroll to Top

The calculators and tools on Formula Factory are provided for general guidance and informational purposes only. Results are estimates based on standard formulas and the values you enter — they do not constitute professional engineering, electrical, or architectural advice. Always verify calculations with a qualified professional before making decisions for any safety-critical, code-compliance, or commercial application. Formula Factory makes no representations or warranties as to the accuracy or completeness of any result, and accepts no liability for errors, omissions, or any outcomes arising from reliance on this information.