Semicircle Area Calculator

A semicircle is half of a full circle. Enter the radius to get the area, the curved arc length, and the total perimeter (arc plus diameter). Handy for circle geometry homework and exam-style questions.

Radius (r)

Distance from the centre to the curved edge

How it works

A semicircle is half of a full circle. Enter the radius to get the area, the curved arc length, and the total perimeter (arc plus diameter). Handy for circle geometry homework and exam-style questions.

The Formula

Area:
A = πr² ÷ 2 Curved length (half circumference):
L = πr Perimeter (arc + diameter):
P = πr + 2r

Worked Example

Worked example
Radius r = 6 cm Area = π × 6² ÷ 2 = 18π ≈ 56.55 cm² Curved length = π × 6 ≈ 18.85 cm Perimeter = 18.85 + 12 ≈ 30.85 cm

Tips, Assumptions & Limitations

The diameter is always twice the radius: d = 2r.
Perimeter includes the straight diameter, not just the curved part.
Area uses the same πr² formula as a full circle, then divide by 2.

FAQ

Area equals half of a full circle: A = πr² ÷ 2, where r is the radius.

Yes. The perimeter is the curved arc (πr) plus the straight diameter (2r), so P = πr + 2r.

Divide the diameter by 2 to get the radius, then enter that value. The calculator works from radius only.

Semicircle area and perimeter show up often in circle topics, composite shapes, and word problems at both GCSE and SAT level.

Companion article

Semicircle Area Calculator: Formula, Examples, and Perimeter

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How this calculator works

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

Worked 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 this tool

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.

Frequently asked questions

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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