Candela to lumens calculator

Enter the luminous flux in lumens, apex angle in degrees and press the Calculate button

to get the luminous intensity in candela:

Candela to lumens calculation

For uniform, isotropic light source, the luminous flux Φ_v in lumens (lm) is equal to the luminous intensity I_v in candela (cd),

times the solid angle Ω in steradians (sr):

Φ_v(lm) = I_v(cd) × Ω_(sr)

The solid angle Ω in steradians (sr) is equal to 2 times pi times 1 minus cosine of half the cone apex angle θ in degrees (°):

Ω_(sr) = 2π(1 - cos(θ/2))

The luminous flux Φ_v in lumens (lm) is equal to the luminous intensity I_v in candela (cd),

times 2 times pi times 1 minus cosine of half the apex angle θ in degrees (°):

Φ_v(lm) = I_v(cd) × ( 2π(1 - cos(θ/2)) )

So

lumens = candela × ( 2π(1 - cos(degrees/2)) )

Or

lm = cd × ( 2π(1 - cos(°/2)) )

Example

Find the luminous flux Φ_v in lumens (lm) when the luminous intensity I_v in candela (cd) is 400cd and the apex angle is 60°:

Φ_v(lm) = 400cd × ( 2π(1 - cos(60°/2)) ) = 336.7 lm