Find quarter circle area and perimeter from radius
Result
Quarter Circle Area
Step-by-Step Derivation
Quarter Circle Area Formula
A = πr² / 4
A quarter circle is one fourth of a full circle. Its area is the circle area divided by four, while its perimeter includes the curved arc and two straight radii.
⚠Radius must be positive. Area is in square units, and perimeter is in the original length unit.
How Quarter Circle Area Works
Start with the full circle formula πr², then divide by four. The boundary has a quarter arc plus the two radii that form the right angle.
Radius
Distance from center to the curved edge.
One Fourth
Area is a quarter of a full circle.
Arc Length
The curved edge is πr/2.
Perimeter
Add the arc and two radii.
💡 Example: For r=8, A=π(8²)/4=50.265 and perimeter=π(8)/2+16=28.566.
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