You can easily calculate the value if calculations with our Candela (cd) to lumens (lm) calculator, check now!

Candela to lumens calculator

You all need is to enter the luminous flux measured in lumens, or the apex angle in degrees and press the = button to measure the luminous intensity in candela:

Candela to lumens calculation

For the uniform, isotropic light source, the luminous flux Φ_{v }measured in lumens (lm), is totally equal to the luminous intensity I_{v} measured in candela (cd), multiplied by the solid angle Ω in the steradians (sr):

Φ_{v(lm)} = I_{v(cd)} × Ω_{(sr)}

The value of solid angle Ω in steradians (sr) is apparently equal to twice the value of pi times 1 minus cosine of the half cone apex angle θ measured in degrees (°):

Ω_{(sr)} = 2π(1 – cos(θ/2))

The luminous flux Φ_{v }measured in lumens (lm) is apparently equal to the luminous intensity I_{v} measured in candela (cd), twice the value of pi times 1 minus cosine of the half apex angle θ measured in degrees (°):

Φ_{v(lm)} = I_{v(cd)} × ( 2π(1 – cos(θ/2)) )

So the value,

lumens = candela × ( 2π(1 – cos(degrees/2)) )

and,

lm = cd × ( 2π(1 – cos(°/2)) )

Conversion from candela to lumens

You can easily calculate the value of luminous intensity in candela (cd) to the luminous flux measured in lumens (lm). It is mandatory that you make note that you can only calculate and not convert the value of candela to lumens, since the value of lumens and candela as they do not represent the same quantity.

Candela to lumens calculation

For the the luminous flux Φ_{v }which is measured in lumens (lm), isotropic light source, uniform is totally equal to the value of the luminous intensity I_{v} which is measured in candela (cd), times the solid angle Ω which is measured in steradians (sr).

Φ_{v(lm)} = I_{v(cd)} × Ω_{(sr)}

The value of solid angle Ω which is measured in steradians (sr) is equal to the twice value of pi which is later multiplied and 1 minus the cosine of half value of cone apex angle θ which is measured in degrees (°):

Ω_{(sr)} = 2π(1 – cos(θ/2))

The luminous flux Φ_{v }which is measured in lumens (lm) is apparently equal to the luminous intensity I_{v} measured in candela (cd),twice multiplied the value of pi times 1 and minus cosine of half the apex angle θ measured in degrees (°):

Φ_{v(lm)} = I_{v(cd)} × ( 2π(1 – cos(θ/2)) )

So, the value of lumens = candela × ( 2π(1 – cos(degrees/2)) )

Or you can say,

lm = cd × ( 2π(1 – cos(°/2)) )

For Example,

Find the value of luminous flux Φ_{v }in lumens (lm), if the luminous intensity I_{v} in candela (cd) is 500cd and the value apex angle is 45°: