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Stadium Shape

Calculate the area and perimeter of a stadium shape (discorectangle/oblong). A rectangle with semicircles on each end. Step-by-step solutions.

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Why: Understanding stadium shape helps you make better, data-driven decisions.

How: Enter Radius (r), Straight Length (a), Total Length (L) to calculate results.

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Stadium Shape Calculator

Calculate area and perimeter of a stadium (discorectangle/oblong). Use radius+straight length or total length+width. Results update automatically.

Calculator Inputs

Semicircle radius
Rectangle length
For display
stadium_calc.out
CALCULATED
Area
76.27 m²
Perimeter
34.85 m
Radius
3 m
Straight (a)
8 m
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Area Breakdown

Step-by-Step Calculation

Given: Radius r = 3 m, Straight length a = 8 m

Area formula: A=πr2+2raA = \pi r^2 + 2ra

Step 1: pir2=piimes32=28.2743pi r^2 = pi imes 3^2 = 28.2743

Step 2: 2ra=2imes3imes8=482ra = 2 imes 3 imes 8 = 48

Step 3: A=28.2743+48=76.2743;extm2A = 28.2743 + 48 = 76.2743 ; ext{m²}

Perimeter: P=2pir+2a=2piimes3+2imes8=34.8496;extmP = 2pi r + 2a = 2pi imes 3 + 2 imes 8 = 34.8496 ; ext{m}

Get AI-Powered Analysis

Analyze your stadium shape dimensions.

For educational and informational purposes only. Verify with a qualified professional.

📋 Key Takeaways

  • • A stadium shape (discorectangle/oblong) = rectangle + two semicircles on opposite ends
  • • Area: A=pir2+2raA = \\pi r^2 + 2ra (circle + rectangle); Perimeter: P=2pir+2aP = 2\\pi r + 2a
  • • From total length L and width W: r=W/2r = W/2, a=L−Wa = L - W
  • • Used for running tracks, pills, pools, rounded UI elements

💡 Did You Know?

🏃Olympic running tracks use stadium geometry. Standard 400 m track: r ≈ 36.5 m, a ≈ 84.4 m.Source: Sports
💊Pills and capsules are often stadium-shaped. Area helps estimate coating or fill volume.Source: Pharma
🏊Many pools and arenas use stadium outlines for rounded ends. Easier to build than full ellipses.Source: Architecture
📱Rounded rectangles in UI design differ: stadium has semicircles; rounded rect has quarter-circles at corners.Source: Design
📐The two semicircles form a full circle of area πr². The rectangle contributes 2ra.Source: Geometry
🔵Stadium perimeter = circumference of full circle (2πr) plus two straight sides (2a).Source: Perimeter

📖 How Stadium Calculations Work

A stadium shape is a rectangle with two semicircles attached to opposite ends. The semicircles share radius r; the rectangle has width 2r and length a. Total area = circle area (πr²) + rectangle area (2ra). Perimeter = full circle circumference (2πr) + two straight sides (2a).

From r and a

A=pir2+2raA = \\pi r^2 + 2ra, P=2pir+2aP = 2\\pi r + 2a

From total length L and width W

r=W/2r = W/2 (width = diameter), a=L−Wa = L - W (length minus curved parts)

🎯 Expert Tips

Use r + a When Available

Radius and straight length are the natural inputs. Use them directly for fastest calculation.

L and W Mode

When you have total length and width, use r = W/2 and a = L − W. Width must be ≤ length.

Units Consistency

Use consistent units (m, cm, in). Area will be in squared units (m², cm²).

Stadium vs Rounded Rect

Stadium = semicircles on ends. Rounded rectangle = quarter-circles at corners. Different formulas.

⚖️ Stadium vs Other Shapes

ShapeCurved PartsArea Formula
Stadium2 semicirclesπr² + 2ra
EllipseFull ellipseπab
CircleFull circleπr²
RectangleNonel × w

❓ Frequently Asked Questions

What if I know total length and width?

Use r = W/2 (width is the diameter) and a = L − W (length minus the curved parts). The calculator has a "Total Length + Width" mode.

Is a stadium the same as a rounded rectangle?

No. A stadium has semicircles on the ends. A rounded rectangle has quarter-circles at the corners. Different shapes, different formulas.

What is the perimeter of a stadium?

P = 2πr + 2a. The two semicircles form a full circle (2πr) plus two straight sides (2a).

Can width exceed length?

No. In L and W mode, width must be ≤ length. Otherwise a = L − W would be negative.

Where are stadium shapes used?

Running tracks, pills/capsules, pools, arenas, and some UI elements.

How do I find r and a from L and W?

r = W/2 (radius is half the width). a = L − W (straight length is total length minus the diameter).

📊 Stadium by the Numbers

2
Semicircles
πr²
Circle area
2ra
Rect area
2πr+2a
Perimeter

⚠️ Disclaimer: This calculator is for educational use. Verify critical measurements with professional tools. Results assume a flat, Euclidean stadium shape.

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