An area of a semicircle calculator finds the area of half a circle. Semicircles appear in architecture, such as arched windows and doorways, in track design, and in geometry problems where a shape is built from a rectangle plus a semicircular end. The calculation is half of a full circle, but the diameter-versus-radius distinction makes it easy to get wrong by a factor of 4 if the diameter is used as if it were the radius.
A semicircle is exactly half of a circle cut along a diameter. Its straight edge is the diameter, and its curved edge is half the circumference. The area is therefore half the area of the full circle with the same radius. That simple relationship is the whole method, and it is why the formula contains a factor of one half in front of pi times radius squared.
What this calculator does
For a semicircle with radius r, area = (pi x r^2) / 2. If the diameter d is given instead, first find r = d / 2, then apply the formula. For example, a diameter of 14 gives radius 7, and area = (pi x 49) / 2 = 76.97 square units. Using 14 directly as if it were the radius would give (pi x 196) / 2 = 307.88, which is four times too large, because radius squared scales by the square of the factor 2.
The calculator below accepts radius directly. Enter the radius in the unit you want, and it returns area in square units, plus the perimeter of the semicircular shape for reference, which is pi x r + 2r, the curved part plus the diameter. Perimeter is not the same as area, and the two should not be confused in a problem that asks for one or the other.
Formula
Area = (pi x r^2) / 2, where r is the radius. If diameter d is given, r = d / 2 first.
How to use it
- Confirm whether the given measurement is radius or diameter. If it is diameter, halve it first.
- Square the radius.
- Multiply by pi, approximately 3.1416.
- Divide by 2 for the semicircle.
- Label the result in square units.
Try the calculator
Worked example
Find the area of a semicircle with radius 7 units. First, r^2 = 49. Then pi x 49 = 3.1416 x 49 = 153.94. Finally, divide by 2: 153.94 / 2 = 76.97 square units. The area is therefore about 76.97 square units. As a check, the full circle with radius 7 has area 153.94, so half of it must be 76.97, which matches.
If the problem had given diameter 14 instead, the first step would be radius = 14 / 2 = 7, and the rest of the calculation would be identical. That halving step is the one most often skipped, and skipping it quadruples the answer.
How to check your answer
Compare with the full circle area. The semicircle area must be exactly half of it for the same radius.
Test with a radius of 1. The semicircle area should be pi / 2, about 1.57, which is a memorable check value.
Check units. Area must be in square units, while the straight edge, the diameter, is in linear units.
Common mistakes
- Using diameter as radius, which makes the area four times too large.
- Forgetting to divide by 2 and reporting the full circle area as the semicircle area.
- Using circumference, 2 pi r, instead of area, pi r^2, in the formula.
- Reporting area in linear units instead of square units.
Frequently asked questions
What is the difference between a semicircle and a half circle?
They are the same shape in most school problems: half of a circle cut along a diameter, with a straight diameter edge and a curved half-circumference edge.
How do I find the perimeter of a semicircle?
Add the curved part, pi x r, to the straight diameter, 2r, giving pi x r + 2r. That is perimeter, not area, and it uses r once, not r squared.
Can I use diameter directly in the formula?
Only after halving it to get radius. The formula needs r, so diameter must be divided by 2 first, otherwise the squared term is four times too large.
