What Is the Semicircle Perimeter?
A semicircle is exactly half of a circle, formed by cutting a full circle along a diameter. Its perimeter (also called its circumference) is the total distance around the boundary of that half-shape. Unlike a full circle, this boundary has two distinct parts: the curved arc that traces half of the original circle, and the straight flat edge along the diameter. Adding these two pieces together gives the complete perimeter.
The Formula Explained
The perimeter of a semicircle is given by:
$$P = \pi r + 2r = r(\pi + 2)$$
Here, \(\pi r\) is the length of the curved arc — half of a full circle's circumference (\(2\pi r \div 2 = \pi r\)). The term \(2r\) is the straight edge, which is simply the diameter of the circle. Factoring out the radius gives the compact form \(r(\pi + 2)\), where \(\pi \approx 3.14159\), so \((\pi + 2) \approx 5.14159\).
How to Use This Calculator
Enter the radius (\(r\)) of the semicircle in any unit of length — centimeters, meters, inches, or feet. Click calculate and the tool returns the total perimeter along with a breakdown showing the curved arc length (\(\pi r\)) and the straight diameter edge (\(2r\)) separately, so you can see how the two parts contribute.
Worked Example
Suppose a semicircle has a radius of 5 units. The curved arc is \(\pi \times 5 \approx 15.708\) units. The straight diameter edge is \(2 \times 5 = 10\) units. Adding them: \(15.708 + 10 = \mathbf{25.708}\) units. Equivalently, $$5 \times (\pi + 2) = 5 \times 5.14159 \approx 25.708.$$
FAQ
Is the perimeter just half the circle's circumference? No. The arc is half the circumference (\(\pi r\)), but you must also add the straight diameter (\(2r\)), since that edge is now part of the boundary.
What if I only know the diameter? Divide the diameter by 2 to get the radius, then use this calculator.
What units does the result use? The perimeter is in the same unit as the radius you entered — there are no fixed units.
