A stadium is a rectangle with a half-circle on each short end: the outline of a running track, a pill, a racetrack conference table or a rounded slot cut by a router. Mathematicians also call it a discorectangle or obround. This calculator finds its area, perimeter and overall size from the end radius and straight length, from the overall length and width, or from the radius together with a known area or perimeter.
How to use the stadium calculator
- Choose from the I know the menu: Radius r and straight length a, Overall length L and width W, Radius r and area, or Radius r and perimeter.
- Enter the values that appear. End radius (r) is the radius of each rounded end, and Straight length (a) is the length of the flat sides between the two half-circles. Overall length (L) and Overall width (W) are tip-to-tip and side-to-side measurements.
- Pick the units. The results list r, a, L, W, the area, the perimeter, and the area split into the rectangle part and the two half-circles.
Stadium formulas
Put the two half-circles together and they make one full circle of radius r. What remains is a rectangle a long and 2r wide. That observation gives every formula:
The last two formulas run the shape backwards. If the area you enter is less than πr², or the perimeter less than 2πr, no straight section could fit, and the calculator says so. With a = 0 the stadium collapses into an ordinary circle.
Worked example: a racetrack conference table
A conference table is 12 ft long and 4 ft wide with fully rounded ends. Choose Overall length L and width W and enter L = 12 and W = 4, in feet.
- End radius: 4 ÷ 2 = 2 ft; straight length: 12 − 4 = 8 ft
- Area: π × 2² + 2 × 2 × 8 = 12.57 + 32 = 44.57 ft² of tabletop to finish
- Perimeter: 2π × 2 + 2 × 8 = 28.57 ft of edge banding, enough for about 14 people at 2 ft each
An elliptical table with the same 12 ft by 4 ft footprint would have only 37.70 ft² of surface, because the ellipse narrows steadily toward its ends while the stadium keeps its full width along the straights.
Running tracks: a stadium in practice
The standard outdoor 400 m track is the best-known stadium shape. The figures below are an approximate illustration, not a substitute for official track-measurement rules. A common design has curves with an inner radius of about 36.5 m. Distance in lane 1 is measured along a line roughly 0.30 m outside the inner curb, so the running radius is about 36.8 m.
Choose Radius r and perimeter, enter r = 36.8 and P = 400, and the calculator returns a straight length of 84.39 m, which matches the straights of that standard design. The two bends account for about 231.2 m of each lap and the straights for the remaining 168.8 m.
Now move out one lane. In lane 2 the measuring line sits about 37.92 m from the center of the bend. Keep a = 84.39 m and the lap grows to roughly 407.04 m. Because the perimeter is 2πr + 2a, the straights don’t matter: each extra meter of radius adds 2π, about 6.28 m per lap, whatever the track’s length. That is why races run in lanes start from a staggered line.
Where else stadiums appear
- Tablets and capsules seen from above, and rounded-end tags and labels.
- Slots and obround holes in sheet metal, which let a bolt slide for adjustment.
- Pools, tubs and racetrack tables, where the shape gives straight sides for seating and soft corners for traffic.
- Cross-sections of capsule tanks: rotate a stadium about its long axis and you get the solid in the capsule calculator.
For the rounded ends alone, use the circle calculator, and for a truly oval outline with no straight sides use the ellipse calculator.
Frequently asked questions
What is a stadium shape?
A stadium is a rectangle with a half-circle attached to each of its short ends, so its outline is two parallel straight sides joined by two semicircles. It is also called a discorectangle or an obround. The name comes from the outline of an athletics stadium's running track.
Is a stadium the same as an ellipse or an oval?
No. An ellipse curves continuously and has no straight sections, while a stadium has two straight sides joined by circular ends. Many 'racetrack oval' tables and pools are really stadiums, so check whether the long sides are straight before choosing a calculator.
How do I find the perimeter of a stadium?
The two half-circles together make one full circle, so add its circumference, 2πr, to twice the straight length a. A table 12 ft long and 4 ft wide has r = 2 ft and a = 8 ft, giving P = 4π + 16 ≈ 28.57 ft.
Why are the starts on a running track staggered?
Every lane shares the same straights, but each one farther out turns on a larger radius, and a stadium's perimeter grows by 2π for every unit added to the radius. A lane whose radius is about 1.22 m larger adds roughly 2π × 1.22 ≈ 7.7 m per lap, so outer runners start ahead to cover the same distance.
What is the three-dimensional version of a stadium?
Spin a stadium around its long axis and you get a capsule: a cylinder with a hemisphere on each end, like a pill or a propane tank. Use the capsule calculator for its volume and surface area.