How to Find the Radius of a Semi Circle

By Tim Banas
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A semicircle is one half of a circle. It looks like a straight line with a circular arc connecting its ends to one another. The straight edge of the semicircle is the diameter and the arc is half the circumference of a full circle with the same diameter. You can find the radius of a semicircle using the formulas for circumference and diameter. Which formula you use will depend on what information you have been given to start.

Calculating the Radius of a Semicircle With a Known Circumference

Step 1

First, modify the formula for the circumference of a circle to reflect that you are dealing with a semicircle. The formula for the circumference of a circle (C) is as follows:

C = 2 x pi x radius (r)

Since a semicircle is one half of a circle, the circumference of a semicircle is half the circumference of a circle. The formula for the circumference of a semicircle (SC) is the formula for the circumference of a circle multiplied by one half, or 0.5.

SC = 0.5 x 2 x pi x r

Since 0.5 x 2 = 1, you can write the equation this way:

SC = pi x r

Step 2

Now solve the equation for r, since you are trying to solve for radius. Do this by dividing both sides by pi to get r by itself. The result is the following:

r = SC / pi

Step 3

Finally, plug in the value you have been given for the circumference of the semicircle and the value of pi to calculate the radius. For example, if the semicircle has a circumference of 5 centimeters, the calculation would look like this:

r = 5 cm / 3.14 = 1.6 cm

Calculating the Radius of a Semicircle With a Known Diameter

Step 1

First, write the equation for the diameter of a circle, which is the same as the diameter of a semicircle. Since the diameter of a circle, or d, is twice as long as the radius, or r, the equation for diameter is the following:

d = 2r

Step 2

Now rearrange the equation for the diameter of a circle to solve for radius. To solve for r, divide both sides by two. Doing so gives the following:

r = d / 2

Step 3

Finally, plug in the value that you have been given for the diameter of the semicircle. For example, if the diameter has a value of 20 cm the calculation would look like this:

r = 20 cm / 2 = 10 cm

About the Author

Tim Banas started writing professionally in 2009 after teaching high school science for seven years. He has since written and edited for various online publications including Demand Studios, FYILiving.com, Tree.com and BinaryOption.com. He has a Master of Science in biology from Southern Illinois University.