Semicircle Area Calculator: Formula, Examples, and Perimeter
ByMuhammad Ali•Founder of KruskalCode
11:11
6 min read
A semicircle is exactly half of a circle. You will meet it in composite shapes, garden designs, and standard circle geometry questions on GCSE and SAT papers. Once you know the radius, the area and perimeter follow from two short formulas.
Explanation
Picture a full circle cut in half along a diameter. The flat edge is the diameter (length 2r) and the curved edge is half the circumference (πr). The area is half of πr² because you are taking half the circle. Perimeter catches many students out: it is not just the curved part—you must add the diameter as well.
Formula
Area: A = πr² ÷ 2 Curved length: L = πr Perimeter: P = πr + 2r Diameter: d = 2r
Example
Suppose the radius is 6 cm. Area = π × 6² ÷ 2 = 18π ≈ 56.55 cm². The curved length is π × 6 ≈ 18.85 cm. Perimeter = 18.85 + 12 ≈ 30.85 cm (arc plus the 12 cm diameter).
How to use the related calculator
Open the Semicircle Area Calculator and type the radius into the input box. Press calculate to see the area, curved length, total perimeter, and diameter. If a question gives the diameter, divide it by 2 first and enter that as the radius. Compare each line with your manual working to spot arithmetic slips.
Try the related calculator
Open toolFAQ
How do I find semicircle area from the radius?
Square the radius, multiply by π, then divide by 2. In symbols: A = πr² ÷ 2.
Why do I add the diameter to the perimeter?
The boundary of a semicircle runs along the curved arc and the straight diameter. Leaving out the diameter gives you arc length only, not the full perimeter.
How is this different from a full circle area calculator?
A full circle uses A = πr². A semicircle is half of that, so divide the result by 2 or use this dedicated tool.
Can I use this for exam revision?
Yes. Practice with whole-number radii first, then try decimals and fractions. Always state units in your final answer.
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About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
