Candela to lumens conversion calculator

Candela to lumens conversion calculator

Candela (cd) to lumens (lm) calculator and how to calculate.

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

Candela to lumens calculation

For uniform, isotropic light source, the luminous flux Φin 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 Φin 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)) )

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