Lumens to candela calculator

Lumens (lm) to candela (cd) calculator and how to calculate.

Enter the luminous flux in lumens, apex angle in degrees and press the Calculate button to get the luminous intensity in candela:

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

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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 cone apex angle θ in degrees (º):

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 (º):

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

So

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

Or

cd = lm / ( 2π(1 - cos(º/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