Quarter Circle Area Calculator
Compute the area of a quarter circle — one-fourth of a full circle — from its radius, or work backwards to find the radius from a known area.
Solve for
A = πr² / 4
- 1
r²
7² = 49 - 2
π × r²
π × 49 = 153.938 - 3
Area = πr² ÷ 4
153.938 ÷ 4 = 38.4845
How does this calculator work?
Quarter circle area is A = πr²/4 — one-quarter of πr². For r = 7 that is ≈ 38.48 square units. To find the radius from a known area, rearrange to r = √(4A/π). The shape covers exactly 25% of the full circle with the same radius.
Formula
How this is calculated
A quarter circle (or quadrant sector) occupies exactly one-fourth of a full circle, so its area is A = πr²/4 — one-quarter of the standard circle area formula πr². This follows directly from the definition: the sector angle is 90° out of 360° (or π/2 radians out of 2π), giving a fraction of 90/360 = 1/4.
When you know the area and need the radius, the formula inverts to r = √(4A/π). This is useful in design and engineering when you have a fixed area constraint — for example, a quarter-circular bay window, corner flowerbed or foundation footing — and need to find the radius that satisfies it.
The calculator assumes a flat, uniform, solid quarter-circle shape with no thickness. The result is a pure area in squared length units, not a volume. If you also need the perimeter, arc length or centroid of the shape, use the full quarter-circle calculator.
Frequently asked questions
Use A = πr²/4. For example, with r = 7: A = π × 49 / 4 ≈ 38.485 square units. It is exactly one-quarter of the full circle area πr².
Yes. Switch the mode to "Radius (given area)", enter the area, and the calculator returns r = √(4A/π). For example, if A = 50: r = √(200/π) ≈ 7.979.
Yes — a quarter circle is a sector with a central angle of 90°. The general sector area formula A = θr²/2 (θ in radians) gives A = (π/2)r²/2 = πr²/4 for θ = π/2, which is exactly the quarter-circle formula.
Also known as
TG we-Calculate Editorial Team. (2026). Quarter Circle Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/quarter-circle-area-calculator
TG we-Calculate Editorial Team. "Quarter Circle Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/quarter-circle-area-calculator.
TG we-Calculate Editorial Team, "Quarter Circle Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/quarter-circle-area-calculator
@misc{wecalculate_quarter_circle_area_calculator, title = {Quarter Circle Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/quarter-circle-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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