Stage Lighting Beam and Throw
Beam pool diameter at a throw distance, and the center-beam illuminance that lands there.
Example
You enter
- Beam angle (full cone, deg) 20
- Throw distance 30
- Distance unit ft
- Intensity source candela
- Center-beam intensity (candela) 100000
You get
- Beam diameter at target 10.5796
- Center illuminance 111.111
- Illuminance (lux) 1196.01
Checked against published worked examples from: ETC.
Details, formula, and sources
ScopeTheatrical fixture photometry: beam (pool) diameter at a throw distance (2 x throw x tan(beam angle / 2)) and center-beam illuminance by the inverse-square law (E = candela / distance^2, or candela estimated from lumens + beam angle), in footcandles and lux (first-principles point-source photometry, distinct from the architectural lumen-method average).
Formula or tableBeam (pool) diameter = 2 x throw x tan(beam angle / 2); center illuminance E = candela / distance^2 (inverse-square). Candela from lumens = lumens / (2*pi*(1 - cos(beam angle / 2))). 1 fc = 10.764 lux.
Source and editionFirst-principles theatrical photometry - beam spread and the inverse-square illuminance the form fixture photometric charts (manufacturer cut sheets) publish, by name; public domain.
Free accessPublic first-principles photometry. The center-beam candela / field-vs-beam angle come from the fixture's photometric data; a real beam is brighter at center than the edge.
What governsEstimate. AHJ and licensed professional govern.
API field namesbeam_angle_deg, throw_distance, distance_unit, source, candela, beam_diameter_ft, illuminance_fc, illuminance_lux
- Point source single aimed fixture, inverse-square from the photometric center; no field falloff or atmospheric loss modeledmethod