Lighting calculator
Beam Angle / Throw Distance Calculator
The pool a fixture throws is simple trigonometry: diameter = 2 × throw × tan(angle ÷ 2). A 19° fixture at 30 ft of throw makes a 10 ft circle. Enter the angle from the fixture cut sheet and the throw distance to get the beam size.
Beam angle = 50% intensity edge; field angle = 10%. Use field angle for coverage.
Formulas
Beam diameter
D = 2 × throw × tan(angle / 2)- D:
- pool diameter at the target
- throw:
- fixture-to-target distance along the beam axis
- angle:
- beam or field angle in degrees
How it works
Cut sheets publish two angles. The beam angle bounds the cone where intensity stays above 50% of center, and the field angle bounds 10%. For even wash coverage, design with field angles and overlap adjacent pools roughly to their beam-angle edges; for punchy specials and aerial effects, the beam angle is the number that matters.
Throw is measured along the beam, not across the floor. A fixture at 25 ft trim hitting a spot 20 ft away horizontally has a throw of √(25² + 20²) ≈ 32 ft, and the pool lands as an ellipse when the beam hits at an angle, stretched by roughly 1/cos of the incidence angle in one axis.
PAR cans complicate this pleasantly: their lamps produce oval beams with two different angles (the reference table lists common PAR64 figures), which is why PARs get rotated in their yokes to lay the oval along a stage edge.
Worked example: A 26° ellipsoidal at 40 ft throw, aiming for an 8 ft podium special
- 1.Full field: D = 2 × 40 × tan(13°) = 18.5 ft, far too wide open.
- 2.Shutter or iris down: an 8 ft pool needs an angle of 2 × atan(4/40) = 11.4°.
- 3.A 10° unit (or the 26° with a tight iris, at an intensity cost) makes the shot.
The 26° covers 18.5 ft at that throw; the podium special wants a ~10° beam.
Pool diameter per 10 ft of throw, and typical PAR64 lamp angles
| Angle | Diameter per 10 ft throw | Typical source |
|---|---|---|
| 5° | 0.9 ft | ACL / narrow aerial beam |
| 10° | 1.7 ft | PAR64 VNSP (~9° × 12°) |
| 14° | 2.5 ft | PAR64 NSP (~10° × 14°) |
| 19° | 3.3 ft | 19° ellipsoidal |
| 26° | 4.6 ft | 26° ellipsoidal / PAR64 MFL (~11° × 24°) |
| 36° | 6.5 ft | 36° ellipsoidal |
| 48° | 8.9 ft | PAR64 WFL (~24° × 48°) |
Field notes
- Zoom fixtures list a range (e.g. 12° to 49°): compute both ends before promising a look from a plot.
- Distance eats intensity as well as size; the same fixture at double throw covers 4× the area at a quarter of the lux.
Frequently asked questions
What is the difference between beam angle and field angle?
Beam angle is where intensity falls to 50% of center; field angle is where it falls to 10%. Coverage design uses field angle; the visible hard pool of a profile reads closer to the beam angle.
How big is a 19 degree light at 30 feet?
D = 2 × 30 × tan(9.5°) ≈ 10 ft. The same fixture at 60 ft doubles to a 20 ft pool; beam size scales linearly with throw.
Why is my pool oval instead of round?
Either the beam is hitting the surface at an angle (the pool stretches by about 1/cos of the tilt) or the source is a PAR lamp, which is oval by construction.