How to Calculate Part of a Circle

Protractors are used to find the measurement of an angle.

A circle is a perfectly round shape. The radius is the distance from the center of the circle to any point on the circle. Because the circle is round, every point on the circle will be equidistant from the center. To find the area of part of a circle, you need to know the radius and the sector of the circle that you want to measure. Measuring the area of part of a circle can be useful when you are figuring the amount of ground cover you need for a circle sector.

Things You'll Need

• Protractor
• Ruler or measuring tape

Instructions

1. Measure the circle's radius with the ruler or measuring tape (depending on the size of the circle).

2. Calculate what the area of the circle would be if it were whole by using the formula π*R^2, where R is the radius from step 1. For example, if the radius were 8 inches, you would square eight to get 64 and then multiply 64 by π (approximately 3.14) to get 200.96 square inches.

3. Measure the angle of the part of the circle you want to calculate the area of with the protractor.

4. Divide the angle measure of the sector by 360 to calculate the proportion of the circle you are calculating the area of. For example, if the angle was 45 degrees, you would divide 45 by 360 to get 0.125.

5. Multiply the area of the whole circle (step 2) by the proportion you are looking for (step 4) to calculate the area of part of a circle. Finishing this example, you would multiply 200.96 by 0.125 to get 25.12 square inches.

References

• Math Goodies: Area of a Circle
• Math Warehouse: Area of a Circle