Candela to lumens calculator

Candela (cd) 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 candela:

For uniform, isotropic light source, the luminous flux Φ_v in lumens (lm) is equal to the luminous intensity I_v in candela (cd),

times the solid angle Ω in steradians (sr):

Φ_v(lm) = I_v(cd) × 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 (°):

Ω_(sr) = 2π(1 - cos(θ/2))

The luminous flux Φ_vin lumens (lm) is equal to the luminous intensity I_v in candela (cd),

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

Φ_v(lm) = I_v(cd) × ( 2π(1 - cos(θ/2)) )

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

lm = cd × ( 2π(1 - cos(°/2)) )

See also

Enter Luminous intensity in candela:		cd
Enter apex angle in degrees:		°

Luminous flux result in lumens:		lm