Quarter Circle Perimeter
Calculate quarter circle perimeter using P = pir/2 + 2r. Free geometry tool for arc length and 90-degree sector boundary. Instant results for any radius.
About This Calculator
The quarter circle perimeter calculator computes the total boundary length of a 90-degree circular sector using the formula P = pir/2 + 2r. The perimeter consists of two parts: the curved arc (one-quarter of the circle's circumference) and two straight radial edges (each equal to the radius). This tool is essential for construction, manufacturing, and design projects where accurate edge-length measurements are needed.
The arc length L = pir/2 is derived from the full circumference formula C = 2pir, divided by 4. Adding the two radii gives the complete perimeter. The calculator also displays the arc length separately for applications that only need the curved portion. For example, a quarter circle with radius 10 cm has a perimeter of pi x 10 / 2 + 2 x 10 ≈ 35.71 cm, with an arc length of approximately 15.71 cm.
Enter the radius in any consistent unit (inches, feet, cm, m) -- the perimeter and arc length appear in the same unit. The calculator ensures the radius is positive for valid results. A quarter circle is defined by a central angle of exactly 90 deg, making it a special case of a circular sector. Whether you are measuring trim for curved molding, cutting curved glass, or planning garden edging, this calculator provides the boundary measurement you need.
Frequently Asked Questions
What is the formula for the perimeter of a quarter circle?
The perimeter of a quarter circle is P = pir/2 + 2r, where r is the radius. The arc length is pir/2 and the two straight edges are each equal to the radius. For example, a quarter circle with radius 10 cm has a perimeter of pi x 10 / 2 + 20 ≈ 35.71 cm.
What is the arc length of a quarter circle?
The arc length of a quarter circle is one-quarter of the full circumference: L = pir/2. For radius 8 cm, the arc length is pi x 8 / 2 ≈ 12.57 cm.
Why is the perimeter not simply pir/2?
The perimeter of a quarter circle includes not just the curved arc but also the two straight radial edges. These edges are the two radii that define the quarter circle boundaries, each of length r.
Can I use a diameter instead of radius?
Yes. Divide the diameter by 2 to get the radius, then apply the formula. For a quarter circle with diameter 20 cm, the radius is 10 cm and the perimeter is pi x 10 / 2 + 20 ≈ 35.71 cm.
Where is quarter circle perimeter used in practice?
Quarter circle perimeters are used in construction (curved molding, trim), manufacturing (cutting curved edges), landscaping (border edging for curved garden beds), and design (frames for quarter-circle windows or mirrors).
Is quarter circle the same as a 90-degree sector?
Yes. A quarter circle is a circular sector with a central angle of exactly 90 degrees. Every quarter circle is a sector, but not every sector is a quarter circle -- sectors can have any central angle.