Stadium Shape Area Calculator

A stadium (sometimes called a discorectangle, obround, or pill shape) is a rectangle with a semicircle attached to each short end. Imagine taking a running track and filling in the infield — that’s a stadium.

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 equals the diameter of the semicircular caps.

The rectangle part is l × w; the two semicircles combined make one full circle of radius w/2, so they add π × (w/2)² to the area.

Worked example — athletics track infield: A standard 400 m running track has straightaways of 84.39 m and a width of 73 m between the inside edges of the two curves. The infield (the grass area inside the track):

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

That’s about 1 hectare — roughly the size of a soccer field, which fits because most athletics tracks enclose a regulation soccer field with room around the goal areas.

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 is a smoothly curving oval with no flat sections. They look similar in a quick sketch but have different area formulas:

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

A stadium with l = 0 reduces to a full circle (just the two semicircles joined). An ellipse never has flat sides — it’s always smooth.

Quick check:

If you set l = 0, the stadium formula gives A = π × (w/2)² — exactly the circle area for diameter w. ✓ If w = 0, the formula gives 0 (the shape collapses to a line segment). ✓

Total perimeter is a separate calculation: P = 2l + π × w. That’s the length you’d need for trim or fencing around the shape — covered on the stadium perimeter page.