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)) )