Area of a Semicircle Calculator
This area of a semicircle calculator also gives the perimeter. Example: a semicircle with radius 5 has an area of 39.2699, an arc length of 15.708 and a perimeter of 25.708.
Example: Given: Radius r · Value 5 → Result: Area A = 39.2699 · Perimeter P = 25.708 (radius r = 5). Source: Wikipedia – Semicircle. Updated: .
How it is calculated
A semicircle is half of a disc; it is bounded by a semicircular arc and the diameter.
Formulas
For radius r: area A = π · r² / 2, arc length s = π · r and perimeter P = π · r + 2r, because the boundary also includes the diameter d = 2r. If the area is given instead of the radius, r = √(2A / π); from the perimeter, r = P / (π + 2); from the diameter, r = d / 2. The calculator uses π at full floating-point precision and rounds only for display.
Worked examples
For r = 5, A = π · 25 / 2 = 39.2699, the arc is s = 5π = 15.708 and the perimeter P = 15.708 + 10 = 25.708. The full circle would have an area of 78.5398. With a diameter of 12, r = 6, the area is 56.5487 and the perimeter 30.8496. Conversely, the area 39.2699 leads via r = √(2 · 39.2699 / π) back to the radius 5.
- The area of a semicircle is always exactly half the area of the circle.
- Doubling the radius quadruples the area and doubles the perimeter.
- Typical uses are arched windows, tunnel profiles and semicircular lawns.
Frequently asked questions
How do you find the area of a semicircle?
A = π · r² / 2. For r = 5 that is π · 25 / 2 = 39.2699.
What is the perimeter of a semicircle?
The arc plus the diameter: P = π · r + 2r. For r = 5 that is 15.708 + 10 = 25.708.
How do I get the radius from the area?
With r = √(2A / π). For an area of 39.2699 this gives r = 5.
Sources and legal basis
As of: · Editorial policy
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