How to Calculate the Circumference of a Right Angle

You may need a calculator to find circumference.

Circumference generally refers to the distance around a circle -- sometimes also known as perimeter. In certain instances, however, you may need to calculate the partial circumference of a circle based upon a given central angle. To get this "arc length," you will calculate a portion of your total circumference.

Things You'll Need

• Calculator

Instructions

1. Determine the value of your central angle and radius. For a right angle, the central angle will be 90 degrees. Your radius will depend upon your given diagram or object, measured as the distance from the center of the circle to a point on the circle.

2. Multiply 0.5 times your radius. Because your central angle is 90 degrees, or 90/360 = 1/4 of your circle, you will only need to calculate 25 percent, or .25, of the total circumference. This would be .25(2)(pi)(radius), or more simply, 0.5(radius)(pi).

3. Plug in the approximation for pi, 3.14, and simplify. For example, if your radius was 3 inches, then you would do .5*(3 in.)*(3.14) = 4.71 inches. Thus, your circumference for a central angle of 90 degrees and a radius of 3 inches is 4.71 inches.

Tips & Warnings

• As an alternative to steps 2 and 3, you could more directly multiply 1.57, which is 0.5 x 3.14, to your radius in order to get the partial circumference, or arc length, for any given right angle.

• Formula: 90-degree circumference = 1.57 x radius.

References

• University of Georgia: Arcs, Central Angles, Arc Length & Sector Area