How to Calculate the Area of a Stadium Shape
A stadium shape (also called a discorectangle or capsule) is a rounded rectangle formed by attaching two semicircles to the ends of a rectangle. It is commonly seen in tracks, architecture, and sports fields.
On this page, you'll learn how to calculate the area of a stadium, view a diagram, and use real-world examples. You can also use the embedded Area of a Stadium Calculator for instant results.
What is a Stadium Shape?
A stadium consists of:
- Two identical semicircles on either end
- One central rectangle connecting the semicircles
Area of a Stadium Formula
Let:
r be the radius of the semicirclesl be the length of the rectangle
Total Area = Area of Rectangle + Area of Two Semicircles
Area = 2r × l + π × r²
SVG Diagram of a Stadium Shape
Step-by-Step Example
Given: r = 10 m, l = 30 m
Step 1: Area of Rectangle = 2 × 10 × 30 = 600 m²
Step 2: Area of Circle = π × 10² = 314.16 m²
Total Area: 600 + 314.16 = 914.16 m²
Another Example
Given: r = 5 ft, l = 20 ft
Area of Rectangle = 2 × 5 × 20 = 200 ft²
Area of Circle = π × 5² = 78.54 ft²
Total Area: 278.54 ft²
Use Our Area of a Stadium Calculator
Use the tool below to quickly compute the area based on your inputs:
Launch Area of a Stadium Calculator
- Instant results with any unit
- Responsive and mobile-friendly
- Backed by accurate geometry formulas
Real-Life Uses of Stadium Shapes
- Running tracks
- Football fields with curved ends
- Race courses
- Urban park layouts
- Traffic roundabouts
FAQs
Q: Can I use this formula for elliptical stadiums?
A: No, elliptical stadiums use a different area formula. This calculator is only for shapes with straight sides and semicircular ends.
Q: What unit will the area be in?
A: The output will be in square units of the input (e.g., meters → m², feet → ft²).
