Stadium Shape Area Calculator

A stadium (also called a discorectangle, an obround, or a pill shape) is a rectangle with a semicircle attached to each short end. Take a running track and fill in the infield and you have one.

A = (l × w) + π × (w/2)²

Where l is the straight section length, NOT including the rounded ends, and w is the width, which is also the diameter of the semicircular caps.

The rectangle part is l × w. The two semicircles combine into one full circle of radius w/2, so they add π × (w/2)² between them.

Worked example: athletics track infield A World Athletics standard 400 m track has straights of 84.39 m and a lane-1 kerb radius of 36.5 m, so the enclosed grass is a stadium 73 m wide.

• Rectangle: 84.39 × 73 = 6,160.5 m²
• Two semicircles make one full circle of radius 36.5 m: π × 36.5² ≈ 4,185.4 m²
• Total: 6,160.5 + 4,185.4 ≈ 10,346 m²

Just over a hectare, and noticeably bigger than the football pitch it holds. A full-size 105 × 68 m pitch is 7,140 m², so the infield runs about 45% larger. The pitch fits because its corners tuck into the curved ends: at 34 m off the centre line the cap still reaches 13.3 m past the straight, and the pitch only needs 10.3 m there. It is a tighter fit than it looks from the stands.

Where stadium shapes show up:

• Running tracks and infields. Both the track itself (an annular stadium) and the grass infield are stadium-shaped.
• Pill-shaped pharmaceutical tablets and capsules. The outline of any pill viewed from above.
• Oval rugs and table tops. True ovals (stadium-shaped) are common for dining tables and rugs.
• Race courses and dog-track ovals. Horse races, dog tracks.
• Obround flange gaskets. Industrial sealing flanges for non-circular fittings.
• Storage tank end caps. Some pressure vessels have stadium-shaped manhole covers.

Stadium vs. ellipse, easy to confuse:

A stadium has flat sides connected by half-circle ends. An ellipse curves smoothly the whole way round with no flat sections at all. They look alike in a quick sketch and their area formulas are different:

• Stadium: l × w + π × (w/2)²
• Ellipse: π × a × b, where a and b are the semi-axes

There is a fast way to tell them apart on a real object. Lay a straightedge along the side. If it makes contact over a stretch, the shape is a stadium. If it touches at one point and daylight opens either side of it, the shape is an ellipse.

Quick check:

Set l = 0 and the formula gives A = π × (w/2)², exactly the circle area for diameter w. ✓ Set w = 0 and it gives 0, the shape having collapsed to a line segment. ✓

Total perimeter is a separate calculation: P = 2l + π × w. That is what you need for trim or fencing around the outside, and the stadium perimeter page covers it.