How to Calculate the Square Footage of a Stadium (Capsule) Shape
A stadium — also called a capsule or discorectangle — is a rectangle with a perfect half-circle capping each of its two short ends. It is the shape of a running track infield, many lap pools, rounded traffic islands, and oval rugs. Because the two semicircular ends are identical, putting them together forms one complete circle, which makes the area surprisingly easy to work out: it is simply the rectangle in the middle plus a single full circle.
The stadium area formula
The area combines a rectangle and a circle:
Area = (L × W) + π × (W ÷ 2)²
Here W is the full width of the shape, which is also the diameter of the rounded ends, and L is the length of the straight middle section only. The radius of each semicircle is half the width, so the two ends together contribute the area of one circle, π × radius². This is why you only measure two numbers, even though the shape has curves.
Measuring a stadium shape correctly
The single most common error is measuring the overall length instead of the straight section. Be deliberate about both measurements:
- Straight length (L): Measure only the flat, parallel part in the middle — from the point where one curve begins to where the other curve begins. Do not run the tape all the way to the rounded tips.
- Full width (W): Measure straight across the widest part of the shape. This is the diameter of the end caps, and the calculator halves it to get the radius automatically.
If you accidentally measure the overall length (tip to tip), subtract the width from it to recover the straight section, since the two end caps add up to exactly one width of length.
Worked example
Imagine a backyard lap pool with a straight section of 20 feet and a full width of 10 feet.
Rectangle: 20 × 10 = 200 sq ft. End circle: π × (10 ÷ 2)² = π × 25 ≈ 78.54 sq ft. Total ≈ 278.54 square feet.
For a pool cover or resurfacing estimate, you would add a small margin for fit and trim, typically around 5%, bringing the order to roughly 293 square feet.
Where stadium shapes appear
- Swimming pools: Many residential lap pools are stadiums — straight sides for swimming with rounded ends. Area drives liner, cover and resurfacing costs.
- Running tracks and sports fields: The classic oval track encloses a stadium-shaped infield.
- Traffic islands and roundabail medians: Civil designs use the capsule for smooth, rounded medians.
- Rugs, tabletops and signage: The capsule is a popular design outline where you need area for material.
Related shape calculators
If your shape is fully curved rather than straight-sided, the ellipse calculator is the better fit. For a plain round area use the circle calculator, for a half-circle the semicircle calculator, and for a simple straight-sided pool or patio the rectangle calculator.