Candela
cd
Lumen
lm
Lux
lx
deg
Distance from the source
m
Surface area

# Lumen Calculator (Lumen to Lux to Candela)

By Bogna Haponiuk

If the multitude of units used to describe lighting confuses you, this lumen calculator will surely be of help. You can use it to convert between three most popular units of measuring light: candelas, lumens, and lux. In the article below, we will provide you with some handy formulas that make lux to lumen conversion a piece of cake!

## What are lumens, lux, and candelas?

These three words describe the most commonly used units for measuring lighting. They are all related, but represent entirely different things.

Lumens are a unit of luminous flux, or, in more understandable terms - the total amount of light emitted by a source.

Lux is a measure of the illumination of the surface, or, more clearly - how much light is received by a surface.

Candelas are the SI units of luminous intensity. It is the light emitted from a source in a particular direction, that is - per steradian.

## How to calculate lumens from candelas

Both candelas and lumens are units of emitted light. Knowing one of these two values (either the luminous intensity or the luminous flux), you can easily convert to the other one.

As we mentioned before, candelas are a measure of light emitted per steradian (unit solid angle). It means that this value is independent of the directions in which the light is emitted. Lumens, however, are the total amount of light emitted and depend on the type of light source. For example, a star shines uniformly into all directions. A directional LED lamp (spotlight), however, might give light only to a small area around it.

To convert from candelas to lumens, you have to multiply the value in candelas by the angular span of the light source in steradians:

`lumens = candelas * Ω`

For a light source that emits light uniformly in all directions, `Ω = 4π`.

Steradians are a unit of measuring angles in a 3D space (just like radians for a 2D space). One steradian on a sphere with a radius of one meter gives a surface of one m². Instead of using steradians, you can also describe how the light is emitted with regular 2D angles. Then, you need to know the apex angle θ between two axes that have a common point at the light source:

• the axis at which the light achieves maximal luminosity, and
• the axis at which the light achieves 50% of maximal luminosity.

Then, you can define the angular span as a function of the apex angle:

`Ω = 2π * [1 - cos(θ/2)]`

Finally, you can use this formula for converting between lumens and candelas:

`lumens = candelas * 2π * [1 - cos(θ/2)]`

## Lux to lumen conversion

You can also use this lux calculator for lux to lumen conversion. As mentioned earlier, lumens are a measure of emitted light, while lux - of received light per unit area. It means that the measure of illuminance (on the receiver surface) is the total emitted light in lumens divided by area:

`lux = lumens / area`

If you're wondering how to calculate lumens from lux, you can simply reverse this equation:

`lumens = lux * area`

Illuminance is often expressed in a different unit, called a footcandle. This Imperial unit is directly related to lux:

`1 footcandle = 10.764 lux`

It is also possible to convert between lux and apparent magnitude of a star. The apparent magnitude tells us how bright does the star appear when seen from Earth. For example, a star of apparent magnitude 0 is about 2.08 microlux. The brightest star in our night sky, Sirius, has the apparent magnitude of -1.46, equivalent to 8.17 microlux.

## Convert lux to candlepower

Last but not least, you can use this lumen calculator to convert lux to candlepower (that is, to candelas). As you already know, candelas measure the light emitted in a particular direction, while lux measure the light received per unit area.

We also know that for one steradian, the area of the receiving surface is equal to the squared distance between the source and the receiver. It means that to obtain the value in lux, you have to divide the luminous intensity by the squared distance:

`lux = candela / distance²`

Bogna Haponiuk

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