Stadium Calculator
Calculate the area and perimeter of a stadium shape (discorectangle) — a rectangle capped by two semicircles — from the straight side length and radius.
Frequently Asked Questions
What is a stadium shape?
A stadium (also called a discorectangle or obround) is a rectangle with a semicircle attached to each of two opposite sides. It is the shape of an athletics running track, a pill capsule, or many ice rinks. It is defined by two values: the straight side length (a) and the radius (r) of the semicircular ends.
How do you calculate the area of a stadium?
Area = πr² + 2ra. The two semicircles together form one full circle (πr²), and the central rectangle measures a × 2r. Example: a = 10, r = 3 gives Area = π×9 + 2×3×10 = 28.27 + 60 = 88.27.
How do you calculate the perimeter of a stadium?
Perimeter = 2πr + 2a — the two semicircular ends form a full circle circumference (2πr), plus the two straight sides (2a). A standard 400 m running track is a stadium shape: two 84.39 m straights and two semicircular bends of radius ≈ 36.5 m measured on the inside lane.
Where is the stadium shape used in real life?
Running tracks, ice hockey rinks, pill and capsule design, stadium seating outlines, slot-shaped holes in engineering (drilled slots), UI design (pill-shaped buttons), and architecture. In engineering drawings the shape is usually called an obround or slot.