# Lumen Calculator (Lumen to Lux to Candela)

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:

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:

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:

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:

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:

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:

💡 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**:

- Enter your known value of
**candela**on our calculator. - 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**:

- 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. - 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:

- First,
**remove the value entered for the source radiation angle**. - Then enter a value for
**lux or candela**, whichever is known to you. - 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:

## Want to learn more?

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