# Lumen Calculator (Lumen to Lux to Candela)

Created by Kenneth Alambra
Last updated: Sep 05, 2022

If you're wondering how to convert candela to lumen or lux to lumen, this lumen calculator is for you. Learning about these different photometry quantities is essential when dealing with visible light. Keep on reading to explore:

• What lumen is;
• How to calculate lumens; and
• How to use this candela or lux to lumen calculator.

## What is lumen?

Lumen is a unit of measure for luminous flux, which is the total amount of visible light (within approximately 0.4 to 0.7 µm wavelength) a light source emits. Other than the luminous flux, we also use other photometry quantities to describe the brightness of a light source. In this text, we'll also cover illuminance and luminous intensity and their relationship with luminous flux.

Illuminance (or illumination) is the amount of luminous flux that a particular surface can receive. Let's say a light source emits a luminous flux of 10 lumens to a surface with an area of 2 square meters. The illumination that the surface receives is equal to 10 lumens per 2 square meters or 5 lumens per square meter (or lm/m²). We can also use lux as its unit of measure, where 1 lux equals 1 lumen per square meter. We abbreviate lux as lx.

The last photometry quantity on our list is luminous intensity. Luminous intensity is amount of light emission in a particular angular span. That angular span is a two-dimensional angular range we measure in steradians (sr). That said, we measure luminous intensity in units of lumen per steradian (lm/sr) or in candela (abbreviated as cd).

In the next section of this text, let's discuss the relationship of these photometry quantities using equations and some more examples.

## How to calculate lumens

To calculate the luminous flux of a light source, we can use its illuminance and luminous intensity. Using illuminance as our known photometry quantity, all we have to do is multiply its value by the area the light source illuminates, as shown below:

$\small \Phi_v = E_v\times A$

Where:

• $\Phi_v$ is the luminous flux in lumens;
• $E_v$ is the illuminance in lux; and
• $A$ is the ** area** receiving the luminous flux.

Let's say we want to illuminate a $\small{10\text{-m}^2}$ room with $\small{300\ \text{lux}}$ of lighting. We can find the needed lumens of lighting by substituting these values to our formula, as shown below:

\small \begin{align*} \Phi_v &= E_v\times A\\ &= 300\ \text{lx}\times 10\ \text{m}^2\\ &= 3000\ \text{lm} \end{align*}

For that room, we can use four 750-lumen LED bulbs to meet that illumination.

On the other hand, we can multiply the light source's luminous intensity, $I_v$, by its angular span, $\Omega$. In equation form, we can express that as follows:

$\small \Phi_v = I_v\times\Omega$

A light source that radiates in all directions, like a non-directional bulb or candlelight, has an angular span equal to $4\pi\ \text{steradians}$.

We can also determine the equivalent angular span of a light source if we can determine its beam or apex angle, which we can denote as $\theta$, as we can see in this equation:

$\small \Omega = 2\pi\times (1 - \cos{\tfrac{\theta}{2}})$

We determine the apex angle by finding the angle between the axis where the light is brightest (directly across the light source and the surface it is directed to) and the axis where the light shines 50% of its brightest luminosity.

By combining the lux to lumens conversion formula and the apex angle to angular span formula, we arrive at this equation:

$\small \Phi_v = I_v\times2\pi\times (1 - \cos{\tfrac{\theta}{2}})$

So if we want to install a $\small{500\ \text{candela}}$ (or $\small{500\ \tfrac{\text{lm}}{\text{sr}}}$) lightbulb with an apex angle of $\small{120\degree}$ (or $\small{\tfrac{2}{3}\pi\ \text{radians}}$) in the middle of a room's ceiling, we can find it's equivalent luminous flux in lumens as follows:

\small \begin{align*} \Phi_v &= I_v\times2\pi\times (1 - \cos{\tfrac{\theta}{2}})\\[0.5em] &= 500\ \tfrac{\text{lm}}{\text{sr}}\times2\pi\times (1 - \cos{\tfrac{\tfrac{2}{3}\pi}{2}})\\[0.8em] &= 500\ \tfrac{\text{lm}}{\text{sr}}\times2\pi\times (1 - \cos{\tfrac{2\pi}{6}})\\[0.9em] &= 500\ \tfrac{\text{lm}}{\text{sr}}\times2\pi\times \left(\frac{1}{2}\right)\\[0.9em] &= 500\ \tfrac{\text{lm}}{\text{sr}}\times\pi\ \text{sr}\\[0.5em] &= 500\pi\ \text{lm}\\[0.5em] &= 1570.796\ \text{lm}\\[0.5em] &≈ 1570.8\ \text{lm} \end{align*}

💡 Besides in units of lux (an SI unit), we can also express illuminance values in the Imperial units of "footcandle". The relationship between lux and footcandle is every 1 footcandle is equal to 10.764 lux.

Now that we know how to calculate lumens, whether from candela to lumen or lux to lumen, let us discuss how to use this lumen calculator.

## How to use this candela or lux to lumen calculator

To use this tool as candela to lumen calculator:

1. Enter your known value of candela on our calculator.
2. Input your light source radiation angle or apex angle. Our tool has a default value of 360° that you can change to any angle you like.

On the other hand, to use this tool as a lux to lumen calculator:

1. Enter your desired illumination. You can also change the illumination units like kilolux, mircrolux, or footcandles, to name a few other units available in our tool.
2. Type in the area of the surface that will receive the light.

Upon doing these steps, you will already see the equivalent luminous flux of the values you entered on our tool.

You might be wondering what the variable distance from the source is for. That is for the direct conversion from lux to candela or vice versa. So aside from being a candela or lux to lumen calculator, this tool also works as a lux to candela calculator. For that:

1. First, remove the value entered for the source radiation angle.
2. Then enter a value for lux or candela, whichever is known to you.
3. Lastly, input the distance from the source of light to the surface receiving the light to find either lux or candela.

To manually convert illuminance, $E_v$, in lux to luminous intensity, $I_v$, in candela, given a distance, $d$, you can use this equation:

$\small I_v = E_v\times d^2$

Perhaps you want to learn about the luminosity of stars. We have our luminosity calculator waiting for you.

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