Case 1
- Radius
- 5
19.634954
Open with these valuesQuarter Circle Area Calculator
19.634954units²
Result: 19.634954 units²A quarter circle is the wedge a 90° angle sweeps out, so its area is πr² ÷ 4. Radius 5 gives 19.634954 square units. Careful with the perimeter: it is not a quarter of the circumference, because the two straight radii belong to the boundary too — πr ÷ 2 + 2r.
Worked examples
How it's calculated
A = π × r² ÷ 4
- StepMeasure the radius — either straight edge of the quarter.
- StepEnter it in any length unit.
- ResultRead the area in the square of that unit.
Reference table
| Radius | Exact, arc, perimeter | Area |
|---|---|---|
| 0.5 | π ÷ 16, 0.785398, 1.785398 | 0.196350 |
| 1 | π ÷ 4, 1.570796, 3.570796 | 0.785398 |
| 2.5 | 1.5625π, 3.926991, 8.926991 | 4.908739 |
| 5 | 6.25π, 7.853982, 17.853982 | 19.634954 |
| 10 | 25π, 15.707963, 35.707963 | 78.539816 |
Questions
How do I calculate the area of a quarter circle?
Square the radius, multiply by π, then take a quarter. For a radius of 5 that is π × 25 ÷ 4 = 19.634954 square units. It is simply one fourth of the full circle's πr².
Why is the perimeter bigger than the arc length?
The perimeter is the whole boundary: the curved arc plus the two straight radii that meet at the corner, so πr ÷ 2 + 2r. For a radius of 5 that is 7.853982 + 10 = 17.853982. Forgetting the two straight sides is the most common mistake when fencing or framing the shape.
What is the arc length of a quarter circle?
A quarter of the full circumference 2πr, which simplifies to πr ÷ 2. For a radius of 5 it is about 7.853982. That is the curved edge only.
How does a quarter circle compare to a full circle?
It is exactly one fourth of it — four quarter circles of the same radius fit together into one complete disc. So the area is always πr² ÷ 4 and the arc is always 2πr ÷ 4.
What units does the quarter circle calculator use?
Any length unit you like. Enter the radius in centimetres and the area comes back in square centimetres; the arc and perimeter stay in plain centimetres.
Sources and last check
Information, not professional advice.