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
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:
Where r is the radius. 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.
Since 0.5 × 2 = 1, you can write the equation this way:
Now solve the equation for r, since you are trying to solve for radius. Do this by dividing both sides by π to get r by itself. The result is the following:
Finally, plug in the value you have been given for the circumference of the semicircle and the value of π to calculate the radius. For example, if the semicircle has a circumference of 5 centimeters, the calculation would look like this:
Calculating the Radius of a Semicircle With a Known Diameter
Remember that π is a constant that is equal to approximately 3.14.
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:
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:
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: