Candela to lumens conversion calculator

Insert the luminous flux in lumens, apex angle in degrees and press the Calculate button to get result the luminous intensity in candela.

Enter Luminous intensity in candela:		cd
Enter apex angle in degrees:		°
Luminous flux result in lumens:		lm

Candela to lumens manual calculation

luminous flux Φv in lumens (lm) is equal to the luminous intensity Iv in candela (cd), multiplied by solid angle Ω in steradians (sr).

Φv(lm) = Iv(cd) × Ω(sr)

Solid angle Ω in steradians (sr) is equal to 2 pi times 1 minus cosine of half the cone apex angle θ in degrees (°)

Ω(sr) = 2π(1 - cos(θ/2))

luminous flux Φv in lumens (lm) is equal to the luminous intensity Iv in candela (cd), multiplied by 2 times pi times 1 minus cosine of half the apex angle θ in degrees (°)

Φv(lm) = Iv(cd) × ( 2π(1 - cos(θ/2)) )

So

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

Or

lm = cd × ( 2π(1 - cos(°/2)) )