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