# How to convert lumens to candela

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

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

### Lumens to candela calculation

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

divided by the solid angle Ω in steradians (sr):

Iv(cd) = Φv(lm) / Ω(sr)

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

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

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

So

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

Or

cd = lm / ( 2π(1 - cos(°/2)) )

#### Example

Find the luminous intensity Iv in candela (cd) when the luminous flux Φv in lumens (lm) is 337lm and the apex angle is 60°:

Iv(cd) = 337 lm / ( 2π(1 - cos(60°/2)) ) = 400.3 cd

Candela to lumens calculation ►