Semicircle Area Calculator
A semicircle area calculator helps you find the space inside half a circle, plus the curved arc length and full perimeter, from one radius value. Enter the radius and the tool returns the area in square units, the arc length for the rounded edge, the diameter across the flat side, and the total perimeter for the closed shape. That matters for school problems, patio layouts, arched windows, and any job where you need to know both surface coverage and edge length. People usually remember that a semicircle is half of a circle, but they often miss that the perimeter still includes the straight diameter along the bottom.
Quick answer
A semicircle is one half of a full circle cut exactly along its diameter.
Area
39.2699
Arc length
15.708
Perimeter
25.708
Diameter
10
What this tells you
- •A semicircle is one half of a full circle cut exactly along its diameter.
- •Its area is half of the circle area, so the formula is pi times radius squared divided by 2.
- •Its curved edge is half of the full circumference, so the arc length is pi times the radius.
- •Its full perimeter is the curved edge plus the flat diameter, which gives pi r + 2r.
- •If you only know the width across the flat side, that width is the diameter, so divide it by 2 before using the radius field.
- •Area is measured in square units, while arc length, perimeter, and diameter stay in the same plain unit as the radius.
How to Use
- 11. Enter the radius of the semicircle. If your measurement is the full width across the flat side, divide that diameter by 2 first.
- 22. Read the main area result to see how much surface the semicircle covers in square units.
- 33. Check the arc length result when you only need the curved top edge, such as trim, edging, or rounded framing.
- 44. Check the perimeter result when you need the full closed outline, because that value adds the curved edge and the straight bottom edge.
- 55. Keep your units consistent. A radius in inches gives area in square inches, while a radius in meters gives area in square meters.
How It Works
Formula
A = pi r^2 / 2, arc length = pi r, perimeter = pi r + 2rThe calculator follows the same logic as the formula file. A full circle has area pi r squared, so a true half circle has area pi r squared divided by 2. The curved edge is half of a full circumference, so the arc length is pi r. The perimeter of the whole shape is not just the curve. It is the curved arc plus the straight diameter, which equals pi r + 2r. For a radius of 5, the area is pi x 25 / 2 = 39.2699, the arc length is pi x 5 = 15.7080, and the perimeter is 15.7080 + 10 = 25.7080. Rounded to two decimals, those become 39.27, 15.71, and 25.71.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Radius 5 semicircle
Use A = pi r squared / 2 with r = 5. That gives pi x 25 / 2 = 39.2699, which rounds to 39.27. The same radius gives an arc length of 15.71 and a full perimeter of 25.71 after adding the 10 unit diameter.
Semicircular window over a 36 inch door
A 36 inch span means the radius is 18 inches. The area is pi x 18 squared / 2 = pi x 324 / 2 = 508.9380, which rounds to 508.94 square inches. The curved edge is 56.55 inches, and the full perimeter is 92.55 inches when the 36 inch bottom edge is included.
Half-circle patio 4 meters across
A patio that is 4 meters wide has a radius of 2 meters. The area is pi x 2 squared / 2 = pi x 4 / 2 = 6.2832, so the paved surface is about 6.28 square meters. The rounded edge alone is 6.28 meters, while the full border is 10.28 meters.
Garden bed with radius 7.5 feet
For r = 7.5, square the radius first to get 56.25. Then compute pi x 56.25 / 2 = 88.3573, which rounds to 88.36 square feet. The curved edge is 23.56 feet, and the complete perimeter is 38.56 feet after adding the 15 foot diameter.
Semicircle from a 14 centimeter diameter
Start by turning the 14 centimeter diameter into a 7 centimeter radius. The area is pi x 7 squared / 2 = pi x 49 / 2 = 76.9690, so the rounded result is 76.97 square centimeters. The arc length is 21.99 centimeters, and the perimeter is 35.99 centimeters.
Semicircle Measurements by Radius
Use these common radius values as a quick check for homework, sketches, and estimating jobs. Area values are square units. Arc length and perimeter stay in the same unit as the radius.
| 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. A semicircle's perimeter is the curved half-circumference plus the straight diameter.
- Typing the diameter into the radius field. If the shape is 10 units across, the radius is 5, not 10, and that difference changes the area by a factor of 4.
- Using half the circumference as the full outline. Pi r gives the arc length only, not the closed perimeter.
- Forgetting that area uses square units. A radius measured in feet produces square feet, not plain feet.
- Applying the formula to an arch that is not a true half circle. Flattened or taller arches are different shapes and need segment or custom geometry formulas.
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