# Arc length, how to calculate

How to calculate the length of an arc. radians or degrees with examples!

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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) = (Θ ÷ 360) x (2 x π x r)

or

A = (Θ ÷ 360) x (D x π)

Where:

A = Arc length

Θ = 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

Θ = 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 ÷ 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 π 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 Θ

Where:

A = length of arc

r = radius of circle

Θ = 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

Θ = 2.094 It’s pretty simple, just multiply the radius by the angle

A = 5m x 2.094 radians = 10.47m

#### 4 COMMENTS

1. i had to look at so many sites before coming to this one and i actually understood how it works looking at this, ty