Semicircle Area Calculator
Enter the radius, diameter, area, arc length, or perimeter of a semicircle and every other measurement fills in automatically. Switch between metric and imperial units. The step-by-step panel shows exactly how each result was computed from the value you provided.
Formula
Worked example
A semicircle with radius 5 cm: Area = π × 5² / 2 = π × 25 / 2 ≈ 39.27 cm². Arc = π × 5 ≈ 15.71 cm. Perimeter = 15.71 + 10 ≈ 25.71 cm (arc plus the straight diameter edge).
What is a semicircle?
A semicircle is exactly half of a circle, created by cutting along a diameter. It has one curved edge (the arc, which is half the full circle circumference) and one straight edge (the diameter). Because it is half a circle, its area is always half the area of the full circle with the same radius: A = πr² / 2. The perimeter is NOT half the circle perimeter. It is the arc length plus the diameter: P = πr + 2r = r(π + 2). Forgetting to add the diameter is the single most common error when calculating the perimeter of a semicircle.
How to use this calculator
Choose the measurement you already know from the "I know the" dropdown: radius, diameter, area, perimeter, or arc length. Enter its value and the calculator instantly fills in all the other measurements. Switch between metric and imperial units using the unit selector at the top. The step-by-step panel below the results shows the exact arithmetic used to derive each value, so you can verify or adapt the working for your own notes.
Semicircle area and perimeter formulas explained
The area formula A = πr² / 2 comes directly from the full-circle area formula A = πr², halved because a semicircle is half a circle. The arc length (the curved part) is πr, which is half of 2πr, the full circumference. The perimeter of a semicircle includes both the arc and the straight diameter edge: P = πr + 2r. Factoring out r gives P = r(π + 2) ≈ 5.14r. So the perimeter of a semicircle is always about 5.14 times its radius.
Solving for radius from other measurements
This calculator works in reverse for all five measurements. Given the area: r = √(2A / π). Given the perimeter: r = P / (π + 2). Given the arc length: r = arc / π. These reverse formulas are derived by rearranging the primary equations. All three are exact, not approximations, because they come from the same definitions. The calculator applies the appropriate formula depending on which value you select in the dropdown.
Real-world uses of semicircle geometry
Semicircles appear in architecture (arched doorways and windows), engineering (tunnel cross-sections and pipe halves), interior design (rugs and bay windows), and sports (the D-zone on a soccer or hockey pitch). The area formula tells you how much material covers the face of the shape. The perimeter formula tells you how much trim or edging you need to go around the boundary. If you only need the curved edge, use the arc length formula alone.
Semicircle measurements for common radii
| Radius | Diameter | Area | Arc length | Perimeter |
|---|---|---|---|---|
| 1 | 2 | 1.57 | 3.14 | 5.14 |
| 2 | 4 | 6.28 | 6.28 | 10.28 |
| 3 | 6 | 14.14 | 9.42 | 15.42 |
| 4 | 8 | 25.13 | 12.57 | 20.57 |
| 5 | 10 | 39.27 | 15.71 | 25.71 |
| 6 | 12 | 56.55 | 18.85 | 30.85 |
| 8 | 16 | 100.53 | 25.13 | 41.13 |
| 10 | 20 | 157.08 | 31.42 | 51.42 |
| 15 | 30 | 353.43 | 47.12 | 77.12 |
| 20 | 40 | 628.32 | 62.83 | 102.83 |
All values use the exact formulas A = πr²/2, arc = πr, P = r(π+2). Rounded to 2 decimal places.
Frequently asked questions
Is the perimeter of a semicircle the same as half the circle circumference?
No. The perimeter of a semicircle includes the straight diameter edge as well as the curved arc. The arc alone is half the circle circumference (= πr), but the perimeter adds the diameter (= 2r), giving P = r(π + 2). For a semicircle with radius 5, that is 5 × 5.1416 ≈ 25.71 units, not just the arc of 15.71 units.
What is the area of a semicircle with diameter 10?
A diameter of 10 means a radius of 5. Area = π × 5² / 2 = 25π / 2 ≈ 39.27 square units. You can verify this with the calculator by selecting "Diameter" and entering 10.
How do I find the radius if I only know the area?
Rearrange A = πr² / 2 to get r = √(2A / π). For example, an area of 50 gives r = √(100 / π) = √(31.83) ≈ 5.64. Select "Area" in the dropdown and type 50 to see all the other measurements.
What is the difference between arc length and perimeter of a semicircle?
The arc length is only the curved part of the semicircle boundary: arc = πr. The perimeter is the total boundary, including the straight diameter edge: P = πr + 2r. Use arc length when you need to measure or cut just the curved edge; use perimeter when you need to go all the way around the shape.
How does the semicircle area compare to the full circle area?
A semicircle has exactly half the area of the full circle with the same radius. Full circle: πr². Semicircle: πr² / 2. This is always true, regardless of the radius or units.
Can I use this calculator for both metric and imperial units?
Yes. Select your preferred unit system at the top of the calculator. The results are shown in the same unit you enter, so if you enter 5 inches you get the area in square inches and lengths in inches.