The area of a sector can be calculated with the following formula:

If calculated in degrees:

**A = (Θ ÷ 360) x (Π x r ^{2})**

If calculated in radians:

**A = 0.5 x r ^{2} x Θ**

Where

A = Area

Θ = Angle (measured in radians or degrees)

Π = Pi (3.14)

r = radius

360 = A Constant

0.5 = A Constant

## Example (In Degrees)

You’ve been asked to calculate the area of a sector when the **radius** of the circle is **5m** and the angle is **120 degrees**.

**r = 5m**

**Θ = 120**

**A = (Θ ÷ 360) x (Π x r ^{2})**

**A = (120° ÷ 360) x (Π x 5 ^{2})**

**A = (0.33333) x (Π x 25)**

**A = (0.33333) x (78.5398)**

**A = 26.18m ^{2}**

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**

Then we calculated the area of the full circle using (Π x r^{2}) and then multiplied the area of the full circle by the percent of the circle we actually have, to give us the area of the sector.

## Example (In Radians)

You’ve been asked to calculate the area of a sector when the **radius** of the circle is **5m** and the angle is **2.094 radians**.

**r = 5m**

**Θ = 2.094**

**A = 0.5 x r ^{2} x Θ**

**A = 0.5 x 5 ^{2} x 2.094**

**A = 0.5 x 25 x 2.094**

**A = 12.5 x 2.094**

**A = 26.18m ^{2}**