What is a stadium shape?
A rectangle with a semicircle on each end — the shape of a running track's inner boundary, an athletics field, or a slot in machined metal. It is sometimes called a discorectangle or obround. The two semicircles together form one complete circle, which is what makes the formulas simpler than they first look.
How is the area calculated?
Rectangle plus circle: area = (length × width) + πr², where r is half the width and the length is the straight section only. Because the two semicircular ends combine into a full circle, you add πr² once rather than computing two halves. The commonest error is including the curved ends in the straight length, which double-counts.
How is the perimeter calculated?
Twice the straight length plus the circumference of the full circle: P = 2L + 2πr. The curved ends contribute one whole circumference between them. For a running track this is why lane 1's inner line is 400 m while outer lanes are longer — the straights are identical but the curve radius grows with each lane.
Why do running tracks stagger the starting positions?
Because each lane's curved section has a larger radius, adding roughly 2π times the lane width per lap — about 7.04 m for a standard 1.22 m lane. Over one lap, lane 8 would run some 50 m further than lane 1 if all started level. Staggered starts equalise the total distance, which is a direct application of this perimeter formula.
What is the difference between a stadium and an ellipse?
They look similar but are not the same. A stadium has two straight sections joined by circular arcs, so its curvature is constant on the ends and zero on the straights. An ellipse has continuously varying curvature and no straight portion. Athletics tracks are stadiums, not ellipses — which matters, because the formulas for an ellipse's perimeter have no simple closed form.
Where else does this shape appear?
Slotted holes in engineering drawings, where a bolt needs adjustment room; capsule-shaped tablets; skate parks; agricultural irrigation patterns; and the rounded rectangles common in interface design, though those usually use arcs at the corners rather than full semicircular ends.