# How to convert candela to lumens

How to convert luminous intensity in candela (cd) to luminous flux in lumens (lm).

You can calculate but not convert candela to lumens, since lumens and candela do not represent the same quantity.

### 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

Lumens to candela calculation ►