Area of Semicircle Calculator
Enter the radius of a semicircle, or its diameter or perimeter, to find its area.
Updated
Area of Semicircle Calculator
Our Area of Semicircle Calculator halves the area of a full circle, πr² ÷ 2, to give the area of a half circle in square units. Know the diameter or the perimeter instead? Switch the input and it works the area out from that, with the arc length, perimeter and the area in other units.
Quick answer
The area of a semicircle is A = πr² ÷ 2: π × 7² ÷ 2 = 24.5π ≈ 76.97 cm².
- From the diameter: A = πd² ÷ 8, so a 10 m diameter gives ≈ 39.27 m²
- From the perimeter: r = P ÷ (π + 2), so 36 m gives r ≈ 7.0017 m and ≈ 77.01 m²
- Radius from the area: r = √(2A ÷ π), so 100 m² gives r ≈ 7.979 m
- Half a circle: double the answer for the area of the full circle
What Is the Area of a Semicircle?
A semicircle is half a circle, cut along a diameter. Its area is the flat space inside the curved arc and the straight edge, measured in square units. It is always exactly half the area of the full circle with the same radius.
Area of a Semicircle Formula
A = πd² ÷ 8
- Find the radius. It runs from the centre of the straight edge to the arc.
- Square it. 7 cm × 7 cm = 49 cm².
- Multiply by π. 49 × 3.14159 ≈ 153.94 cm² (the full circle).
- Halve it. 153.94 ÷ 2 ≈ 76.97 cm².
Leave the answer as 24.5π cm² for an exact value. For a whole circle, use the Area of Circle Calculator.
Semicircle Area Examples
| Radius | Diameter | Area |
|---|---|---|
| 1 cm | 2 cm | ≈ 1.57 cm² |
| 3 m | 6 m | ≈ 14.14 m² |
| 5 m | 10 m | ≈ 39.27 m² |
| 7 cm | 14 cm | ≈ 76.97 cm² |
| 6 in | 12 in | ≈ 56.55 in² |
| 10 ft | 20 ft | ≈ 157.08 ft² |
Doubling the radius makes the area 4 times bigger: a 10 ft semicircle covers 4 times the area of a 5 ft one.
Area From the Diameter
The diameter is the straight edge of the semicircle, so the radius is half of it. Halve it and use πr² ÷ 2, or use πd² ÷ 8 in one go:
A = π × 5² ÷ 2 ≈ 39.27 m²
This is the easiest measurement to take on an arched window or a half-round patio: measure straight across the flat side.
Perimeter and Arc Length
The curved arc is half the circumference, πr. The perimeter adds the straight diameter, 2r, so P = πr + 2r = r(π + 2). To get the area from the perimeter, find r first:
36 ÷ 5.14159 ≈ 7.0017 m
A = πr² ÷ 2 ≈ 77.01 m²
Radius From the Area
Double the area, divide by π, then take the square root:
√(200 ÷ π) ≈ 7.979 m
Double it for the diameter: a semicircle of 100 m² is about 15.96 m across its straight edge.
Common Mistakes
- Forgetting to halve. πr² is the full circle; a semicircle is half of it.
- Using the diameter as the radius. The answer comes out 4 times too big.
- Leaving out the straight edge. The perimeter is πr + 2r, not just the arc πr.
- Forgetting square units. The answer is 76.97 cm², not 76.97 cm.
Key Terms
- Semicircle
- Half a circle, cut along a diameter.
- Radius
- Centre to arc, r.
- Diameter
- The straight edge, 2r.
- Arc length
- The curved edge, πr.
- Perimeter
- Arc plus diameter, πr + 2r.
How to Use the Area of Semicircle Calculator
- Choose what you know. Pick Radius, Diameter or Perimeter. Radius is the usual choice; Diameter is the straight edge, and Perimeter is the arc plus the straight edge.
- Enter the value. Type it, such as 7, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). Decimals and fractions such as 3/4 work.
- Read and copy the result. The area appears as you type, with a drawing, the working, the exact value in terms of π, the arc length, perimeter, full circle area and the area in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: an arched window is 1.2 m wide along its base. Choose Diameter, enter 1.2 and pick m. The area is about 0.565487 m², the radius is 0.6 m and the arc is about 1.884956 m long.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the area of a semicircle?
Square the radius, multiply by π and halve it. A semicircle with a 7 cm radius has an area of π × 49 ÷ 2 ≈ 76.97 cm².
What is the formula for the area of a semicircle?
A = πr² ÷ 2, where r is the radius and π ≈ 3.14159. With the diameter d it is A = πd² ÷ 8.
How do you find the area of a semicircle from the diameter?
Halve the diameter to get the radius, then use πr² ÷ 2. A 10 m diameter gives r = 5 m and an area of about 39.27 m².
What is the perimeter of a semicircle?
The curved arc plus the straight diameter: P = πr + 2r. A semicircle with a 7 cm radius has a perimeter of about 35.99 cm.
How do you find the radius of a semicircle from its area?
Double the area, divide by π and take the square root. An area of 100 m² gives r = √(200 ÷ π) ≈ 7.979 m.
Is the area of a semicircle half the area of a circle?
Yes. A semicircle is a circle cut in half along a diameter, so its area is exactly half of πr².
Is the Area of Semicircle Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Area of Semicircle Calculator to find the area of any half circle from its radius, diameter or perimeter, in any units.