Math
Semicircle Calculator
A semicircle is half a circle, so its area is half of πr² and its curved edge is half of 2πr.
The semicircle calculator returns the area, the arc length, and the full perimeter (arc plus diameter — the part people forget) exactly in terms of π and as decimals, from any one of radius, diameter, area, or perimeter.
Area is in square units; the rest are lengths.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Area
—
- Area (exact)
- —
- Arc length
- —
- Perimeter (arc + diameter)
- —
- Radius
- —
- Diameter
- —
- Centroid height above the flat side
- —
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Study path
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What the semicircle calculator solves
A semicircle is half a circle, so its area is half of πr² and its curved edge is half of 2πr. The semicircle calculator returns the area, the arc length, and the full perimeter (arc plus diameter — the part people forget) exactly in terms of π and as decimals, from any one of radius, diameter, area, or perimeter.
Formula
How to use it
- Choose the measurement you know: radius, diameter, area, or the full perimeter.
- Enter it and pick a unit.
- Read the area (exact and decimal), arc length, and perimeter. The perimeter already includes the straight diameter edge.
How to read the answer
The area is half the full circle's area and shows as a multiple of π when the radius is a nice number (r = 4 gives 8π). The arc length is only the curved edge; the perimeter adds the straight diameter across the bottom, which is why P = πr + 2r.
Common mistakes and edge cases
- Forgetting the diameter in the perimeter. The curved part alone is πr; the full boundary is πr + 2r.
- Halving the circumference and calling it the area — arc length and area are different quantities with different units.
- Using the diameter in πr²/2 without halving it first.
- A zero or negative measurement cannot form a semicircle.
Worked examples
Radius 4 (area 8π)
Area
25.1327
Diameter 10 cm
Area
39.2699
Area 50 in²
Area
50
Perimeter 20 ft
Area
23.7676
Decimal radius 2.5 m
Area
9.8175
Zero diameter (impossible)
Area
Error
Frequently asked questions
What is the area of a semicircle?+
Half the area of the full circle: A = πr²/2. With radius 4 the area is 8π ≈ 25.13 square units.
What is the perimeter of a semicircle?+
The curved arc plus the straight diameter: P = πr + 2r = r(π + 2). For r = 4 that is 4π + 8 ≈ 20.57.
Is the arc length of a semicircle half the circumference?+
Yes. The full circumference is 2πr, so the semicircle's arc is πr. But the arc is not the whole perimeter — add the diameter for that.
How do I find the radius from the area of a semicircle?+
Solve A = πr²/2 for r: r = sqrt(2A/π). Area 50 gives r ≈ 5.642.
Where is the centroid of a semicircle?+
On the line of symmetry, 4r/(3π) ≈ 0.4244r above the flat edge. Engineers use it for center-of-mass problems.
How do I find the radius from the perimeter?+
Divide by (π + 2): r = P / (π + 2) ≈ P / 5.1416. A perimeter of 20 gives r ≈ 3.89.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026