Stadium Shape Perimeter Calculator

A stadium has two straight sides of length l and two semicircular ends of width w. The perimeter combines the straights with one full circle of curved boundary:

P = 2l + π × w

The two semicircles combine to one full circle’s worth of circumference (πw, where w is the diameter), and the two straight sides contribute 2l.

Worked example — 400 m running track: A standard outdoor running track is designed so the inside-lane perimeter is exactly 400 m. With a width of 73 m (the lane-1 inside curve has radius 36.5 m): Solve P = 2l + π × 73 = 400 → 2l = 400 − 229.34 → l = 85.33 m of straightaway.

Most modern tracks use 84.39 m straights with slightly different curve geometry, but the same principle: total perimeter = 2 × straight + full circle of curve.

Where stadium perimeter matters in practice:

• Track length. Race distances on outdoor tracks are measured around the stadium-shaped inside line.
• Oval rug or carpet trim. Tape edging for an oval rug uses the stadium perimeter formula.
• Pill mold tooling. Pharmaceutical and confectionery molds for capsule-shaped products.
• Race-car circuit fencing. Oval racetracks need fence material around the outside.
• Aquarium edge molding. Stadium-shaped aquariums use the perimeter for top-trim or LED strip length.

The “track lanes” gotcha:

Outside lanes on a track are longer because their stadium has bigger l and bigger w. If lane 1 is 400 m, lane 8 (about 9 m further out radially) traces a stadium with w about 18 m greater. The extra perimeter is roughly π × 18 ≈ 56.5 m per loop. That’s why 400 m races on a track use staggered starts — outer lanes start further forward to even out the distance.

Quick sanity checks:

• l = 0: P = π × w, which is just the circumference of a circle with diameter w. ✓
• w = 0: P = 2l (the shape collapses to a line segment back and forth). ✓
• l → very large: perimeter is mostly 2l (the curved ends become a small fraction of the total). The shape looks like a long thin oval.

Stadium vs. ellipse perimeter:

Stadium perimeter is a clean closed form: 2l + πw. Ellipse perimeter has no clean formula — it uses approximations like Ramanujan’s. If your shape has flat sides, it’s a stadium; if it smoothly curves, it’s an ellipse. Don’t apply stadium math to elliptical layouts.