The Stadium Calculator finds area and perimeter of a stadium shape (also called a discorectangle): a rectangle with semicircles on opposite ends. Enter semicircle radius r and straight length a between the curved ends. The page redraws a labelled figure with r and a marked.
Overall length tip-to-tip is a + 2r; overall width is 2r. Related pages cover the 3D cousin on the Capsule Calculator, the Circle Calculator for the end disks, and the Rectangle Calculator for the middle band alone.
Calculate the area of a stadium
Area splits into a central rectangle plus two semicircles that together make one full circle. The straight length a is the distance between the flat portions of the parallel sides, not including the curved ends. Radius r sets the semicircle size at both ends. The Stadium Calculator adds those parts.
A = pi * r^2 + 2 * a * rThe rectangle has width 2r and length a, so its area is 2 * a * r. The two semicircles form one circle of area pi * r^2. Doubling a grows only the rectangular contribution; doubling r grows both parts, with the circle term quadratic in r.
For a = 10 and r = 3:
A = pi * 9 + 2 * 10 * 3 = 9 * pi + 60 approx 88.27Exact form 9 * pi + 60 is preferred when later steps keep pi. A common error is to use overall length a + 2r as if it were the rectangle length, which double-counts the ends.
Calculate the perimeter
Perimeter walks one semicircle arc, a straight side, the opposite semicircle arc, and the remaining straight side. The curved contribution is one full circumference 2 * pi * r while the straight parts contribute 2 * a. The Stadium Calculator reports that closed outline length.
P = 2 * pi * r + 2 * aPerimeter scales linearly with both a and r. There is no pi * r^2 term on the perimeter; that belongs to area only.
For a = 10 and r = 3:
P = 2 * pi * 3 + 2 * 10 = 6 * pi + 20 approx 38.85Running-track lane length for one lap often matches this perimeter when a and r describe the lane centerline. Confirm whether the measured radius is to the curb or to the lane center before ordering distances.
Solve a stadium with radius 3 and length 10
Use r = 3 and straight length a = 10 as the reference stadium. Overall length is 16; overall width is 6. Area and perimeter follow. 1. Overall size
Overall length = a + 2*r = 16
Overall width = 2*r = 62. Area
A = 9 * pi + 60 approx 88.273. Perimeter
P = 6 * pi + 20 approx 38.85These numbers share r = 3 and straight length 10 with the Capsule Calculator's cylindrical height fixture, but the capsule reports 3D volume 126 * pi, not this planar area. Keep the worked examples on their own pages.
Understand the stadium and capsule relationship
A stadium is the two-dimensional outline. A capsule extrudes that profile into three dimensions with a cylindrical midsection and hemispherical ends. Volume and surface area of the solid live on the Capsule Calculator page. Area and perimeter of the outline live here.
Cross-section through the long axis of a capsule is a stadium with the same r and straight length. That shared silhouette is why the pages cross-link as a family. They do not share formulas: multiplying stadium area by a thickness is not capsule volume.
Search queries that say "stadium" may mean a sports arena building; this page means the geometric discorectangle. Sports-field problems that need only the track outline still fit these area and perimeter formulas once a and r are measured.
Overall bounding box area is (a + 2r) * 2r = 2r(a + 2r). For a = 10 and r = 3 that box is 96, while stadium area is only about 88.27. The difference is the four corner regions outside the semicircles. Using the bounding rectangle as if it were the stadium overstates area by those corners.
When a track has staggered lanes, each lane has its own effective radius. Perimeter grows by about 2 * pi * (lane offset) per lane for a full lap when straights share length a. The Stadium Calculator models one outline at a time; compute each lane separately with its own r.
Frequently asked questions
What is stadium area?
Stadium area is A = pi * r^2 + 2 * a * r. For a = 10 and r = 3, A = 9 * pi + 60 approx 88.27.
What is stadium perimeter?
Perimeter is P = 2 * pi * r + 2 * a. For a = 10 and r = 3, P = 6 * pi + 20 approx 38.85.
What is length a?
Length a is the straight segment between semicircles, not the overall tip-to-tip length. Overall length is a + 2r.
How does a stadium relate to a capsule?
A stadium is the 2D capsule silhouette. Use the Capsule Calculator for 3D volume and surface area.
Is a stadium the same as a running track?
A standard track outline is a stadium. Lane length uses the perimeter formula with the lane's effective radius and straight length.
Can the Stadium Calculator start from overall length?
Yes. If overall length L and radius r are known, a = L - 2r when L > 2r, then area and perimeter follow.
What units does the Stadium Calculator use?
Radius and length share one length unit. Area uses square units; perimeter uses length units.
Why not use (a+2r) by 2r as a bounding rectangle?
That rectangle over-counts the corners outside the semicircles. Use the rectangle-plus-circle formula instead.
What is overall width?
Overall width is 2r, the diameter of the end semicircles. Overall length is a + 2r.
Can area start from overall length L?
Yes. Set a = L - 2r when L > 2r, then A = pi*r^2 + 2*a*r.
Is a capsule cross-section a stadium?
Yes. An axial cross-section of a capsule is a stadium with the same r and straight length. Volume still belongs on the Capsule Calculator.
What is the reference stadium area?
For a = 10 and r = 3, area is 9 * pi + 60 approx 88.27 and perimeter is 6 * pi + 20 approx 38.85.
How much does the bounding box over-count?
For the reference inputs the bounding rectangle area is 96 while stadium area is about 88.27. The gap is the four outer corners.
Summary
Stadium Calculator returns area and perimeter for a discorectangle from semicircle radius and straight length, with substituted arithmetic and a labelled figure. Worked numbers match a = 10 and r = 3: A = 9 * pi + 60 and P = 6 * pi + 20.
Use the Capsule Calculator for the 3D pill solid and the Circle Calculator for the end disks alone.