# 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