Quarter Circle Perimeter Calculator

The perimeter of a quarter circle is P = (pi x r) / 2 + 2r, where r is the radius. The term (pi x r)/2 is the arc length, which is one quarter of a full circumference (2 x pi x r divided by 4), and 2r is the two straight edges, each exactly one radius long.

Use radius 10: arc length = pi x 10 / 2 = 15.707963; two straight edges = 2 x 10 = 20; perimeter = 15.707963 + 20 = 35.707963, about 35.71.

Yes. First halve the diameter to get the radius (r = d/2). For diameter 14, r = 7, the arc is pi x 7 / 2 = 10.995574, and the perimeter is 10.995574 + 14 = 24.995574, about 25.00.

Yes. Recover the radius with r = sqrt(4A / pi). For example, a quarter circle with area 25 x pi = 78.539816 gives r = sqrt(4 x 78.539816 / pi) = 10, so the perimeter is pi x 10 / 2 + 20 = 35.707963, about 35.71.

The curved side alone is L = (pi x r) / 2. For radius 8 the arc is 12.566371, while the full perimeter adds the two straight edges (2 x 8 = 16) for a total of 28.566371. Do not confuse arc length with perimeter.

The area is A = (pi x r^2) / 4, one quarter of the full circle area pi x r^2. For radius 10 the area is pi x 100 / 4 = 78.539816, about 78.54 square units.

The boundary of a quarter circle includes two straight sides along the radii, not only the curve. The arc alone is about 1.5708 x r, but the full perimeter is about 3.5708 x r, which is (pi/2 + 2) times the radius. Forgetting the two radii undercounts the perimeter by more than half.

Rearrange P = r x (pi/2 + 2) to get r = 2P / (pi + 4). For a perimeter of 35.707963, r = 2 x 35.707963 / (pi + 4) = 10.

No. A semicircle (half circle) has perimeter P = pi x r + 2r, because its curved side is half the full circumference. A full circle is 2 x pi x r. This calculator covers the 90-degree quarter circle only.

Any consistent unit works: centimeters, meters, inches, feet, and so on. The perimeter comes out in the same unit as the input, and the area in square units of that unit. Mixing units in one calculation is not allowed.

All math runs in your browser using double-precision floating point (about 15 to 16 significant decimal digits), far beyond what a tape measure or ruler can resolve. Results are rounded to 4 decimals for display, with 6 decimals in the worked steps.

Quarter-circle geometry appears in rounded building corners, arch and window trim, quarter-round molding profiles, landscaping beds, pipe bend layouts, and machine parts with filleted corners. Perimeter is what you need for trim, edging, or molding lengths; area is what you need for material coverage.