Find stadium shape area and perimeter from radius and straight length
Result
Capsule Area
Step-by-Step Derivation
Capsule Area Formula
A = πr² + 2ra
A capsule shape combines a rectangle with two semicircles. The two semicircles make one full circle, so the area is circle area plus the rectangle area.
⚠Radius and straight length must be positive. The straight length is the length between the rounded ends, not the full overall length.
How Capsule Area Works
Think of the shape as a rectangle of width 2r and length a, plus two half circles. Combining the halves gives the πr² term.
Radius
Controls the rounded end size.
Straight Length
Distance between the two rounded ends.
Rectangle Part
Middle area is 2ra.
Round Ends
Two semicircles equal one circle.
💡 Example: For r=3 and a=10, A=π(3²)+2(3)(10)=88.274 and perimeter=38.85.
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