Stadium Shape Calculator
Calculate area and perimeter of a stadium shape, a rectangle with semicircular ends.
Enter the cap radius and straight-section length for instant results.
Stadium Shape (Discorectangle)
A stadium shape, also called a discorectangle or an obround, is a rectangle with a semicircle attached to each of its two shorter ends. That gives a closed shape with no corners anywhere on its boundary. Think of a running track seen from above, the outline of a capsule pill, or the slot a bolt slides along in a piece of adjustable steelwork.
Do not call it an oblong. That word means a rectangle longer than it is wide, and reaching for it here is how the flat-sided and the round-ended versions get mixed up on a drawing.
Defining the shape:
- a = radius of the semicircular ends (also = half the width of the rectangle)
- b = length of each straight section (the rectangular middle part only)
- Total shape width = 2a
- Total shape length = b + 2a
Formulas:
| Property | Formula |
|---|---|
| Area | A = pi * a^2 + 2 * a * b |
| Perimeter | P = 2 * pi * a + 2 * b |
| Total Length | L = b + 2a |
| Total Width | W = 2a |
Understanding the formulas:
- Area = (full circle of radius a) + (rectangle of width 2a and length b)
- Perimeter = (full circle circumference) + (two straight sections)
Worked example, a track-sized outline (a = 40 m, b = 80 m):
- Area: pi × 1600 + 2 × 40 × 80 = 5,027 + 6,400 = 11,427 m^2
- Perimeter: 2pi × 40 + 2 × 80 = 251.3 + 160 = 411.3 m
- Total length: 80 + 80 = 160 m
- Total width: 80 m
A real 400 m athletics track is not these numbers, and it is worth knowing why. The standard has 84.39 m straights on a 36.5 m kerb radius, so a = 36.5 and b = 84.39, which gives a boundary of 398.12 m rather than 400. The missing 1.88 m comes from measuring the lap 30 cm outside the kerb, where a runner actually travels.
Special case, a perfect circle: When b = 0 the stadium collapses to a circle of radius a. Area = pia^2 and Perimeter = 2pi*a, so both formulas reduce correctly. ✓
Where this shape appears: Athletics tracks, capsule pills in plan view, running-track infields, slotted bolt holes in steelwork and machine plate, oval rugs and dining tables, obround flange gaskets, and the cross-section of a flat oval duct.
Be careful with sports pitches, which are a common mistake here. A rugby field and an American football field are both plain rectangles; only the track wrapped around the outside is a stadium shape. Computational geometry uses the same figure under yet another name, the capsule, as the region swept by a circle moving along a line segment, which makes it the cheapest useful shape for collision tests.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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