Quarter Circle Calculator
Find the area and perimeter of a quarter circle.
A quarter circle is one-fourth of a full disk, bounded by two radii and an arc.
How the Math Works
A quarter circle is one-fourth of a complete circle, formed by two radii and the arc connecting them. To find its area, we take one-fourth of the area of a full circle (πr²), giving us the formula: area = ½πr². For the perimeter, we must include both straight edges (the two radii, each of length r) and the curved edge (one-fourth of the circumference, which is ½πr). Adding these together: perimeter = ½πr + 2r.
Practical Applications
To use this calculator practically, first measure or determine the radius of the quarter circle. For example, if designing a quarter-circle garden bed with a radius of 3 meters, plug r = 3 into the area formula to find you need approximately 7.07 square meters of soil, and use the perimeter formula to calculate that you'll need about 13.71 meters of edging material for all three sides.
Day-to-Day Use
This calculation appears in everyday situations like determining how much material you need for quarter-circle projects—whether it's concrete for a circular patio corner, fabric for a curved cushion, paint for a rounded wall section, or grass seed for a quarter-circle lawn area. It's also useful for estimating costs when contractors need to price materials based on area, such as flooring, tiles, or roofing sections with curved edges.
Worked example
Radius 6 → area ≈ 28.27, perimeter ≈ 21.42.
FAQ
Why add 2r to the perimeter?
A quarter circle is bounded by the arc and the two radii forming the corner.