# Millicandela to lumens calculator

Millicandela (mcd) to lumens (lm) 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 millicandela:

### Millicandela 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 millicandela (mcd),

times the solid angle *Ω* in steradians (sr) divided by 1000:

*Φ*_{v(lm)} = *I*_{v(mcd)} × *Ω*_{(sr)} / 1000

The solid angle *Ω* in steradians (sr) is equal to 2 times pi times 1 minus cosine of half the 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 millicandela (mcd),

times 2 times pi times 1 minus cosine of half the apex angle *θ* in degrees (°) divided by 1000:

*Φ*_{v(lm)} = *I*_{v(mcd)} × ( 2π(1 - cos(*θ*/2)) ) / 1000

So

lumens = millicandela × ( 2π(1 - cos(degrees/2)) ) / 1000

Or

lm = mcd × ( 2π(1 - cos(°/2)) ) / 1000