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.

For uniform, isotropic light source, the luminous intensity *I*_{v} in candela (cd) is equal
to the luminous flux Φ_{v }in lumens (lm),

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

*I*_{v(cd)} = *Φ*_{v(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 *I*_{v} in candela (cd) is equal to the luminous flux Φ_{v }in lumens (lm),

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

*I*_{v(cd)} = *Φ*_{v(lm)}
/ ( 2π(1 - cos(*θ*/2)) )

So

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

Or

cd = lm / ( 2π(1 - cos(°/2)) )

Find the luminous intensity *I*_{v} in candela (cd) when the luminous flux Φ_{v }
in lumens (lm) is 337lm and the apex angle is 60°:

*I*_{v(cd)} = 337 lm / ( 2π(1 - cos(60°/2)) ) = 400.3 cd

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