# Lumens to candela calculator

Lumens (lm) to candela (cd) calculator and how to calculate.

Enter the luminous flux in lumens, apex angle in degrees and press the *Calculate* button to get the luminous intensity in candela:

### Lumens to candela calculation

For uniform, isotropic light source, the luminous intensity *I*_{v} in candela (cd) is equal
to the luminous flux Φ_{v }in lumens (lm),

divided by the solid angle *Ω* in steradians (sr):

*I*_{v(cd)} = *Φ*_{v(lm)} / *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 (º):

*Ω*_{(sr)} = 2π(1 - cos(*θ*/2))

The luminous intensity *I*_{v} in candela (cd) is equal to the luminous flux Φ_{v }in lumens (lm),

divided by 2 times pi times 1 minus cosine of half the apex angle *θ* in degrees (º):

*I*_{v(cd)} = *Φ*_{v(lm)} / ( 2π(1 - cos(*θ*/2)) )

So

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

Or

cd = lm / ( 2π(1 - cos(º/2)) )

#### Example

Find the luminous intensity *I*_{v} in candela (cd) when the luminous flux Φ_{v }
in lumens (lm) is 337lm and the apex angle is 60°:

*I*_{v(cd)} = 337 lm / ( 2π(1 - cos(60°/2)) ) = 400.3 cd