What Is a Semicircle?
A semicircle is exactly half of a circle, formed by cutting a circle along a diameter. It has one curved edge (the arc) and one straight edge (the diameter). Because it is half a circle, its area is simply half the area of the full circle, while its perimeter combines the curved arc with the straight diameter rather than half the circle's circumference.
How to Use This Calculator
Enter the radius (\(r\)) of the semicircle — the distance from the center of the straight edge to the curved edge. The calculator instantly returns the area, the full perimeter, the arc length of the curved side, and the diameter of the straight side. Make sure your radius is in consistent units; the area will be in those units squared.
The Formula Explained
The area of a full circle is \(\pi r^{2}\). Since a semicircle is half of that, the area is:
$$A = \frac{\pi r^{2}}{2}$$The perimeter is the curved arc plus the straight diameter. The arc of a semicircle is half the circle's circumference (\(\pi r\)), and the diameter is \(2r\), giving:
$$P = \pi r + 2r$$
Worked Example
Suppose the radius is 5 units. The area is
$$\frac{\pi \times 5^{2}}{2} = \frac{\pi \times 25}{2} \approx 39.27 \text{ square units.}$$The arc length is \(\pi \times 5 \approx 15.71\) units, the diameter is \(2 \times 5 = 10\) units, and the perimeter is \(15.71 + 10 \approx 25.71\) units.
FAQ
Is the perimeter just half the circle's circumference? No. You take half the circumference (the arc, \(\pi r\)) and add the diameter (\(2r\)), because the flat side is now part of the boundary.
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter that value.
What units does the result use? The area is in your input units squared (e.g. cm²), and the perimeter, arc, and diameter are in the same linear units you entered.
