# Candela to lumens calculator

Convert luminous intensity in candelas (cd) to total light output in lumens (lm) effortlessly. Ideal for lighting design, LED specifications, and illuminance calculations. Accurately convert candela to lumens using this convenient online tool.

## what is Candela to lumens

Candela (cd) and lumens (lm) are both units used to measure aspects of light, but they represent different properties.

Candela (cd) is a unit that measures the luminous intensity of a light source in a specific direction. It quantifies how bright a light appears to an observer in a particular direction.

Lumens (lm), on the other hand, represent the total amount of visible light emitted by a light source, regardless of the direction it is emitted in. Lumens measure the overall brightness or intensity of the light source.

To convert from candela to lumens, you typically need additional information about the light source, specifically its beam angle. This is because the luminous flux (measured in lumens) depends on both the luminous intensity (measured in candelas) and the distribution of light within the beam angle.

The formula to convert candela to lumens is:

Luminous Flux (lm) = Luminous Intensity (cd) * Solid Angle (in steradians)

The solid angle represents the portion of a sphere covered by the light source's beam angle, measured in steradians.

It's important to note that the conversion from candela to lumens involves considering the light source's characteristics and the angular distribution of its emitted light. Therefore, a direct conversion without knowledge of the beam angle is not possible.

## Candela to lumens calculation

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

times the solid angle *Ω* in steradians (sr):

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

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

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

So

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

Or

lm = cd × ( 2π(1 - cos(°/2)) )

### Candela to lumens Example#1

Find the luminous flux Φ_{v }
in lumens (lm) when the luminous intensity *I*_{v} in candela (cd)
is 400cd and the apex angle is 60°:

*Φ*_{v(lm)} = 400cd × ( 2π(1 - cos(60°/2)) ) = 336.7 lm

### Candela to lumens Example#2

Assuming you have a light source with different luminous intensities in Candela (cd) and you want to convert them to Lumens (lm), you can use the following table:

Luminous Intensity (cd) | Solid Angle (sr) | Luminous Flux (lm) |
---|---|---|

1000 | 4π | 12566 |

500 | 4π | 6283 |

200 | 4π | 2513 |

100 | 4π | 1256 |

To convert the luminous intensity to luminous flux, simply multiply the luminous intensity by the solid angle for each value.

For example, if the luminous intensity is 1000 cd and the solid angle is 4π sr, the luminous flux would be 1000 cd * 4π sr = 12566 lm.

Similarly, for a luminous intensity of 500 cd and a solid angle of 4π sr, the luminous flux would be 500 cd * 4π sr = 6283 lm.

You can follow the same calculation for other values in the table.

Please note that this conversion assumes a spherical distribution of light and equal brightness in all directions. In practice, the actual luminous flux may vary depending on the specific characteristics of the light source.