# Lumens to millicandela calculator

Lumens (lm) to millicandela (mcd) 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:

## Lumens to millicandela calculation

For uniform, isotropic light source, the luminous intensity *I*_{v} in millicandela (mcd) is equal
to 1000 times the luminous flux Φ_{v }in lumens (lm),

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

*I*_{v(mcd)} = 1000 × *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 apex angle *θ* in degrees (°):

*Ω*_{(sr)} = 2π(1 - cos(*θ*/2))

The luminous intensity *I*_{v} in millicandela (mcd) is equal
to 1000 times 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 (°):

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

So

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

Or

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