# 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 Φin lumens (lm),

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

Iv(cd) = Φv(lm) / Ω(sr)

So 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))

So The luminous intensity Iv in candela (cd) is equal to the luminous flux Φin 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 1

Find the luminous intensity Iv in candela (cd) when the luminous flux Φin lumens (lm) is 340lm and the apex angle is 60°:

Iv(cd) = 340 lm / ( 2π(1 - cos(60°/2)) ) = 403.9 cd

#### Example 2

Find the luminous intensity Iv in candela (cd) when the luminous flux Φin lumens (lm) is 360lm and the apex angle is 60°:

Iv(cd) = 360 lm / ( 2π(1 - cos(60°/2)) ) = 427.6 cd

#### Example 3

Find the luminous intensity Iv in candela (cd) when the luminous flux Φin lumens (lm) is 380lm and the apex angle is 60°:

Iv(cd) = 380 lm / ( 2π(1 - cos(60°/2)) ) = 451.4 cd

#### Example 4

Find the luminous intensity Iv in candela (cd) when the luminous flux Φin lumens (lm) is 440lm and the apex angle is 60°:

Iv(cd) = 440 lm / ( 2π(1 - cos(60°/2)) ) = 522.6 cd

#### Example 5

Find the luminous intensity Iv in candela (cd) when the luminous flux Φin lumens (lm) is 540lm and the apex angle is 60°:

Iv(cd) = 540 lm / ( 2π(1 - cos(60°/2)) ) = 641.4 cd

Candela to lumens calculation ►