Quarter Circle Calculator — Area, Arc Length & Perimeter
Enter the radius of a quarter circle (90° sector) to instantly get its area, arc length, total perimeter and centroid distance from the right-angle corner.
A = πr² / 4
- 1
r²
5² = 25 - 2
π × r² (full circle area)
π × 25 = 78.5398 - 3
Area = πr² ÷ 4
78.5398 ÷ 4 = 19.6350
How does this calculator work?
A quarter circle has area A = πr²/4 and arc length πr/2. The full perimeter (two radii + arc) is 2r + πr/2. Its centroid sits 4r/(3π) ≈ 0.4244r from the right-angle corner along each axis. All values follow directly from one-quarter of the standard circle formulas.
Formula
How this is calculated
A quarter circle is one-fourth of a full circle — a sector with a central angle of exactly 90°. Its area is simply one-quarter of the full circle area, giving A = πr²/4. Because the sector angle is π/2 radians, the arc length (the curved portion) is (π/2) × r = πr/2.
The total perimeter of the quarter-circle shape includes the curved arc and the two straight radial edges that meet at the right angle. Adding the two radii to the arc gives P = 2r + πr/2. This is the total border you would need to measure if you were cutting the shape from sheet material and trimming all three sides.
The centroid — the geometric centre of mass of the flat shape — lies at a distance of 4r/(3π) from the right-angle corner along each axis of symmetry, approximately 0.4244r. This value appears in structural and mechanical engineering when calculating how a quarter-circular cross-section bends. All formulas assume a flat, uniform, solid shape with no thickness.
Frequently asked questions
Arc length is only the curved edge: πr/2. The perimeter is the total boundary of the entire shape — both straight radial edges plus the arc: P = 2r + πr/2. Use arc length when you only need the curved portion (e.g. a road bend); use perimeter when you need the complete border.
Divide the diameter by 2 to get the radius r, then compute A = πr²/4. Equivalently, A = πd²/16, where d is the diameter.
A quarter circle is a circular sector with a central angle of 90° (π/2 radians), also called a quadrant sector. When the shape includes the interior region (as it usually does in area problems), it is simply a quadrant of the circle.
Also known as
TG we-Calculate Editorial Team. (2026). Quarter Circle Calculator — Area, Arc Length & Perimeter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/quarter-circle-calculator
TG we-Calculate Editorial Team. "Quarter Circle Calculator — Area, Arc Length & Perimeter." TG we-Calculate. 2026. https://we-calculate.com/calculator/quarter-circle-calculator.
TG we-Calculate Editorial Team, "Quarter Circle Calculator — Area, Arc Length & Perimeter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/quarter-circle-calculator
@misc{wecalculate_quarter_circle_calculator, title = {Quarter Circle Calculator — Area, Arc Length & Perimeter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/quarter-circle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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