The Trigonometry of Stage Lighting Beams
A theatrical light fixture emits a conical beam of light. The circular footprint diameter (D) on the stage floor is calculated directly from the fixture's beam angle ( heta) and throw distance (T):
The term (2 imes an( heta / 2)) is known in theatrical lighting design as the Beam Multiplication Factor. For a standard 36° ellipsoidal lens, the factor is approximately (0.65). If your lighting electric pipe is 20 feet away, the beam footprint will be (20 imes 0.65 = 13) feet wide.
Beam Angle vs Field Angle
- Beam Angle (50% intensity): The inner cone where illuminance is at least 50% of the center peak intensity. This is the "active punchy" light.
- Field Angle (10% intensity): The outer boundary where light drops down to 10% of peak intensity. Beyond the field angle, the beam drops into darkness.
The Inverse Square Law in Lighting
Illuminance (measured in Foot-candles or Lux) obeys the Inverse Square Law: doubling your throw distance cuts the brightness on stage by 75% (leaving only 1/4 the original light level)! To maintain even face illumination on moving actors, adjacent fixtures must be spaced so their beam angles overlap by at least 20% to 25%.