Stadium Shape and Capsule Calculator (Running Track, Obround, Pill)
Area and perimeter of a rectangle with semicircular ends — a running track, a slot or an obround — and the volume and surface of the matching 3D capsule.
Results
What this tool does
A stadium (also called an obround or slot shape) is two semicircles joined by two straight sides, so it needs only the straight length and the radius. A 400 m lap with bends of 36.5 m radius needs straights of about 85 m, measured on the kerb line — the official measuring line sits a little outside it, so the real figures differ slightly. Spin the same shape around its long axis and you get a capsule: a cylinder with a hemisphere on each end, the shape of a pill, a pressure vessel or a pipe end.
Formula
area = π r² + 2 r ℓ · perimeter = 2π r + 2 ℓ · capsule: V = π r² ℓ + 4/3 π r³, S = 2π r ℓ + 4π r²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sl | Length of the straight part | m |
r | Radius | m |
A | Area of the stadium (flat shape) | m² |
P | Perimeter of the stadium (one lap) | m |
OL | Overall length | m |
OW | Overall width | m |
V | Volume of the capsule (3D) | m³ |
S | Surface area of the capsule (3D) | m² |
Worked example
- Length of the straight part85 m
- Radius36.5 m
- Area of the stadium (flat shape)10,390.39 m²
- Perimeter of the stadium (one lap)399.34 m
- Overall length158.00 m
- Overall width73.00 m
- Volume of the capsule (3D)559,446.704 m³
- Surface area of the capsule (3D)36,235.13 m²
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.