# Candela to lumens calculator

Enter the luminous flux in lumens, apex angle in degrees and press the Calculate button

to get the luminous intensity in candela:

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

Related

### Candela to lumens calculation

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

times the solid angle Ω in steradians (sr):

Φv(lm) = Iv(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 Φv in lumens (lm) is equal to the luminous intensity Iv in candela (cd),

times 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)) )

#### Example

Find the luminous flux Φv in lumens (lm) when the luminous intensity Iv in candela (cd) is 400cd and the apex angle is 60°:

Φv(lm) = 400cd × ( 2π(1 - cos(60°/2)) ) = 336.7 lm