Semicircle Area Calculator

A semicircle is exactly half of a circle, cut along a line through the center, so its area is half the circle's. Semicircles turn up in arched windows, half-round patios, garden beds and the rounded ends of running tracks and pools.

Formula

A = ½ × π × r²

A

the area

π

pi, approximately 3.14159

r

the radius of the full circle

Area from the radius

Square the radius, multiply by π and halve the result. A half-round patio with a radius of 6 ft covers ½ × π × 36 ≈ 56.55 ft². The radius is the distance from the middle of the straight edge out to the top of the curve, which also makes it the height of the semicircle.

Area from the diameter

The straight edge of a semicircle is the full circle's diameter, and it is usually the easiest length to measure. Square it, multiply by π and divide by 8. An arched window 10 ft wide has an area of π × 100 ÷ 8 ≈ 39.27 ft².

• A = π × d² ÷ 8

Perimeter of a semicircle

The perimeter is often misquoted, because it has two parts: the curved edge and the straight edge. The curve is half of the circumference, πr, and the straight edge adds another 2r. A radius of 6 gives a curve of about 18.85 and a perimeter of about 30.85. If you are only edging the curved side of a flower bed, the curve alone is the length to buy.

• Curved edge = π × r
• Perimeter = π × r + 2 × r

Shapes built from a semicircle

Many everyday outlines combine a semicircle with a rectangle. A window with an arched top, for example, is a rectangle with a semicircle on top. Work out each part separately and add them. A running-track infield is a rectangle with a semicircle at each end, and those two ends together form one full circle. Use the rectangle area calculator for the straight section and add the areas.

Frequently asked questions