You can calculate the length of an arc quite simply, but how you calculate it depends if the angle of the arc is measured in degrees or radians.

## Measured in degrees

If the angle of your arc is measured in degrees then use this formula to calculate the length of the arc:

**Arc length (A) = (Î˜ Ã· 360) x (2 x Ï€ x r)**

or

**A = (Î˜ Ã· 360) x (D x Ï€)**

Where:

**A = Arc length**

**Î˜ = Arc angle (in degrees)**

**r = radius of circle**

**D = Diameter of circle**

## Example

You’ve been asked to calculate the length of an arc when the **radius** of the circle is **5m** and the angle is **120 degrees**.

**r = 5m**

**Î˜ = 120**

First we divide the angle by 360. If the arc was a full circle, it would have 360 degrees, but because it is not a complete circle we need to know what **percent of a circle** it is. We do this by diving the angle by the total angle.

**120 degrees Ã· 360 degrees = 0.3333 or 33.33% of a full circle**

Next we calculate the **circumference** of the full circle. **Click here** to learn about how to calculate the circumference of a circle.

**C = 2 x Ï€ x r**

**C = 2 x 3.142 x 5m**

**C = 6.284 x 5m**

**C = 31.42m**

Now we just find what** 33.3%** of the circumference is

**A = 0.3333 * 31.42m = 10.47m**

## Measured in radians

If the angle of your arc is measured in radians then use this formula to calculate the length of the arc:**A = r x Î˜**

Where:

**A = length of arc**

**r = radius of circle**

**Î˜ = angle or arc (in radians)**

## Example

You’ve been asked to calculate the length of an arc when the **radius** of the circle is **5m** and the **angle** is **2.094 radians**.

**r = 5m**

**Î˜ = 2.094** It’s pretty simple, just multiply the **radius** by the **angle**

** A = 5m x 2.094 radians = 10.47m**

[…] Arc length, how to calculate […]

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[…] Figure 6: Arc Length Source: https://theengineeringmindset.com/arc-length-how-to-calculate/ […]