The area of a segment can be calculated using the following formula

If using degrees:

**A = (r ^{2} ÷ 2) x ((Π ÷ 180 x Θ) – sin Θ)**

If using radians:

**A = (0.5 x r ^{2}) x (Θ – sin Θ)**

Where:

A = Area

r = Radius

Π = Pi (3.14)

Θ = Angle

0.5 = A constant

180 = 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**.

**A = (r ^{2} ÷ 2) * ((Π ÷ 180 * Θ) – sinΘ)**

**A = (5^{2} ÷ 2) * ((Π ÷ 180 * 120) – sin120)**

**A =** **(12.5) * ((Π ÷ 180 * 120) – sin120)**

**A =** **(12.5) * ((0.017453**** * 120) – sin120)**

**A =** **(12.5) * ((0.017453 * 120) – sin120)**

**A =** **(12.5) * ((2.0944) – 0.866025)**

**A =** **(12.5) * (1.22837)**

**A = 15.35m ^{2}**

## 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**. (Remember! put your calculator in radians)

**A = (0.5 x r ^{2}) x (Θ – sin Θ)**

**A = (0.5 x 5 ^{2}) x (2.094 – sin 2.094)**

**A = (0.5 x 25) x (2.094 – sin 2.094)**

**A = (12.5) x (2.094 – sin 2.094)**

**A = (12.5) x (2.094 – 0.86622)**

**A = (12.5) x (2.094 – 0.86622)**

**A = (12.5) x (1.22778)**

**A = 15.35m ^{2}**