Example 60 degree beam

Theta is the full beam angle in degrees.

Worked example

Illuminance950.3589 lx

E_lux = I / d^2

Beam diameter1.1547 m

D = 2 × d × tan(theta / 2)

These formulas assume the flux is spread evenly inside the cone. A real lamp does not have that ideal distribution.

Solid angle, candela, and throw

Solid angle 0.8418 sr

Omega = 2 × pi × (1 - cos(theta / 2))

Luminous intensity 950.3589 cd

I = Phi / Omega

Foot-candles 88.2905 fc

E_fc = E_lux / 10.764

Throw to 0.25 lux 61.6558 m

d_throw = 2 × sqrt(I)

Notes only: hallways and stairs 100 lux; office and classroom 300 to 500; drafting 750 to 1000; operating theater 10000 to 50000.

Theta is converted from degrees to radians for cos and tan. The feet form is not applied as a second conversion.