Semicircle Area Calculator
A semicircle with a radius of 5 has an area of 39.27, exactly half the full circle's 78.54. This semicircle area calculator finds the area, the curved arc length, and the full perimeter. The perimeter is the part people get wrong, because it includes the straight edge across the bottom, not just the curve.
Quick answer
A semicircle is half a circle cut along the diameter.
Area
39.2699
Arc length
15.708
Perimeter
25.708
Diameter
10
What this tells you
- •A semicircle is half a circle cut along the diameter.
- •Its area is half the circle formula: pi r squared / 2.
- •The curved edge alone is half the circumference: pi r.
- •The full perimeter adds the flat diameter edge: pi r + 2r.
How to Use
- 1Enter the radius. If you measured across the flat edge, that is the diameter, so halve it first.
- 2Read the area as the main result.
- 3Check the arc length for just the curve, or the perimeter for the whole outline.
- 4Results come out in the square (area) or plain (lengths) of your input unit.
How It Works
Formula
A = pi r^2 / 2, perimeter = pi r + 2rHalving a circle halves its area, so the semicircle formula is the circle's pi r squared divided by 2. For radius 5 that is 78.54 / 2 = 39.27. The perimeter combines the curved half-circumference, pi x 5 = 15.71, with the straight diameter edge of 10, for a total of 25.71.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Radius 5 semicircle
Half of pi times 25. The perimeter is 25.71 including the flat edge.
Semicircular window over a 36 inch door
A transom window spanning a 36 inch frame has a radius of 18 inches.
Half-circle patio, 4 m across
A 4 m wide semicircular patio needs about 6.3 square meters of paving.
Semicircle Measurements by Radius
Area, arc length, and full perimeter for common radii.
| Radius | Area | Arc length | Perimeter |
|---|---|---|---|
| 1 | 1.57 | 3.14 | 5.14 |
| 2 | 6.28 | 6.28 | 10.28 |
| 3 | 14.14 | 9.42 | 15.42 |
| 5 | 39.27 | 15.71 | 25.71 |
| 10 | 157.08 | 31.42 | 51.42 |
Common mistakes
- Leaving the flat edge out of the perimeter. The outline of a semicircle includes the diameter, so the perimeter is pi r + 2r, not just pi r.
- Entering the width as the radius. A semicircle 10 units across has a radius of 5, and squaring the wrong one quadruples the area.
- Halving the circumference and calling it the perimeter. Half the circumference is only the curved part.