Area of a Semicircle Calculator
A semicircle is exactly half a circle. Enter its radius or diameter and get the area, the full perimeter (curved edge plus flat edge), and the arc length.
Example: with I know the Radius (r) · Value 5 → Semicircle area (A): 39.27.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outSemicircle formulas: area and perimeter
A semicircle is half a circle, so its area is half of πr²: A = πr² ÷ 2. With a radius of 5, that’s π × 25 ÷ 2 ≈ 39.27 square units. From a diameter, halve it first (or use A = πd² ÷ 8): a half-circle window above a 36 in wide door has r = 18 and area π × 324 ÷ 2 ≈ 508.94 sq in.
The perimeter of a semicircle is the part people get wrong: it’s the curved edge plus the flat edge, P = πr + 2r. For r = 5 that’s 15.71 + 10 = 25.71 — not half of the full circle’s 31.42, because cutting a circle in half exposes a new straight side (the diameter).
How it’s calculated
Area A = πr² ÷ 2 (from a diameter, r = d ÷ 2 first — equivalent to πd²/8). Perimeter P = πr + 2r, the curved half-circumference plus the straight diameter edge; the curved edge alone is πr. π ≈ 3.14159 via JavaScript’s full-precision Math.PI; rounding only at display.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Halving the circle's circumference for the perimeter — you must add the flat diameter edge: P = πr + 2r.
- Using the diameter as r in πr² ÷ 2 — that makes the area 4× too big; halve it first.
- Reporting area in plain units — semicircle area is in square units (in², ft²).
Frequently asked questions
What is the area of a semicircle formula?
A = πr² ÷ 2. Using the diameter instead, A = πd² ÷ 8 — either way a radius-5 (diameter-10) semicircle covers about 39.27.
How do I find the area of a half circle from its diameter?
Halve the diameter to get r, then apply πr² ÷ 2. A 12 in wide semicircle: r = 6, so A = π × 36 ÷ 2 ≈ 56.55 sq in.
What is the perimeter of a semicircle?
P = πr + 2r ≈ 5.14 × r. For r = 5 that’s 15.71 + 10 = 25.71.
Is a semicircle's area exactly half the circle's?
Yes — the area halves cleanly. Only the perimeter doesn’t, because the straight diameter edge is added when the circle is cut.