# Stadium Calculator

The stadium is a two-dimensional geometric shape build using a rectangle and a pair of semicircles. A rectangle with semicircles at 2 opposite sides is also called a discorectangle, obround, or sausage body. Stadium Calculator is a free handy tool where you can give inputs in the specified input fields of the calculator and press on the calculate button to check the result within no time.

radius | r = |

side length | a = |

perimeter | P = |

area | A = |

### Stadium Formulas

The stadium is a geometric shape having a rectangle with top and bottom lengths whose ends are capped off with semicircles of the radius. The simple and universal formulas to calculate the stadium area, perimeter, side length, radius, and total length are mentioned here. Have a look at these formulas and use them while solving the stadium measurement problems.

**Area of a Stadium Formula:**- Area A = πr² + 2 * r * a

**perimeter of a Stadium formula:**- P = 2 * (πr + a)

**Stadium Height Formula:**- Height h = 2 × r

**Overall length of a Stadium Formula:**- Overall length L = 2 × r + a

**Stadium Calculations:**

Make use of the following additional useful formulas along with the formulas mentioned below to know unknown parameters easily.

- If radius, side length of the stadium are given, then
- Area A = πr² + 2 * r * a
- Perimeter P = 2 * (πr + a)
- Height h = 2 × r
- Overall length L = 2 × r + a

- If area, radius of a stadium are known, then
- Side length a = (A - (πr²)) / (2 * r)
- Perimeter P = 2 * (πr + (A - (πr²)) / (2 * r))
- Height h = 2 * r
- Overall length L = (4r² + A - (πr²)) / (2 * r)

- If side length, perimeter of a stadium are given, then
- Radius r = (P / 2π) - (a / π)
- Area A = πr² + 2 * r * a
- Height h = (2P / π) - (a / π)
- Overall length L = 2 × r + a

- If perimeter, radius of the stadium are given, then
- Side length a = (P / 2) - (πr)
- Area A = πr² + 2 * r * a
- Height h = 2 × r
- Overall length L = 2 × r + a

Where,

a is the side length of a stadium

r is the stadium radius

P is the perimeter

A is the stadium area

h is the stadium height

L is the overall length of a stadium

### Step by Step Process to Find Stadium Area, Perimeter

Follow the simple and easy guidelines listed below to calculate the area, perimeter, radius, side length of a stadium manually.

**Stadium Perimeter:**

- Check outside length, the radius of the stadium from the question.
- Multiply the radius with π and add side length to it.
- Double the result to get the perimeter.

**Stadium Area:**

- Find the stadium radius, length of a side.
- Square the radius and multiply it with π.
- Multiply side length, radius, double the product.
- Add value obtained in steps 2 & 3 to check the area.

**Stadium Radius:**

- Note down the perimeter, length of the side of a stadium.
- Divide the perimeter by double the π value.
- Also, divide side length by π value.
- Subtract values obtained from step 2, step 3 to check the radius.

**Stadium Height:**

- Get the stadium radius.
- Double the radius to get the height.

**Stadium Overall Length:**

- Note down side length, the radius of the stadium.
- Double the radius.
- Add side length to the double radius to check the overall length.

**Stadium Side Length:**

- Process 1:
- Make a note of radius, perimeter.
- Divide the perimeter by 2.
- Subtract it from the product of radius and π.

- Process 2:
- Check radius, the area from the question.
- Multiply π with the square of radius subtract it from the area.
- Double the radius.
- Divide step 2 by step 3 to get side length.

### Example Questions on Stadium

**Example 1: **Find the stadium area, side length, height, overall length? If the stadium radius is 3 cm, the perimeter is 28 cm.

**Solution: **

Given that,

Stadium radium r = 3 cm

Stadium perimeter P = 28 cm

Length of the side a = (P / 2) - (πr)

= (28 / 2) - (3 * π)

= 14 - (3 * 3.14)

= 14 - 9.42 = 4.58 cm

Area A = πr² + 2 * r * a

= π * 3² + 2 * 3 * 4.58

= 9π + 27.58

= 28.26 + 27.58

= 55.84 cm²

Height h = 2 * r

= 2 * 3 = 6 cm

Overall length L = 2 × r + a

L = 2 * 3 + 4.58

= 6 + 4.58 = 10.58 cm

∴ Stadium area is 55.84 cm², radius is 3 cm, perimeter is 28 cm, side length is 4.58 cm, overall length is 10.58 cm, height is 6 cm.

**Example 2: **The stadium side length is 10 feet, the radius is 5 feet. Calculate the stadium area, perimeter, overall length, and height?

**Solution: **

Given that,

Stadium side length a = 10 feet

Radius r = 5 feet

Area A = πr² + 2 * r * a

= π * 5² + 2 * 5 * 10

= 25π + 100

= 25 * 3.14 + 100 = 78.5 + 100

= 178.5 feet²

Stadium Height H = 2 * r

= 2 * 5 = 10 feet

Stadium Overall Length L = 2 × r + a

L = 2 × 5 + 10

= 10 + 10 = 20 feet

Perimeter of a Stadium formula is P = 2 * (πr + a)

P = 2 * (π * 5 + 10)

= 10 π + 20

= 10 * 3.14 + 20 = 31.4 + 20

= 51.4 feet

∴ Stadium side length is 10 feet, the perimeter is 51.4 feet, the area is 178.5 feet², overall length is 20 feet, height is 10 feet and radius is 5 feet.

Areavolumecalculator.com is a best place where you can find calculators of various geometry topics. Have a look at them and use them whenever required to get the instant output.

### Frequently Asked Questions on Stadium Calculator

**1. What are the formulas to find a stadium area, perimeter?**

The stadium perimeter is the sum of the circle's circumference and length of a side. The total area of the stadium is given by the area of the circle formed by combining those two semicircles and the area of the rectangle. Perimeter and area formulas are provided here.

Perimeter P = 2 * (πr + a)

Area A = πr² + 2 * r * a

Where r is the radius, a is the side length of the stadium.

**2. How do you calculate stadium parameters using calculator?**

You have to select one option and enter the required input fields. Later hit on the calculate button of the calculator, it automatically displays area, perimeter, height, overall length, side length for the given values in a short span of time.

**3. What are the geometric properties of a stadium?**

The stadium is a two-dimensional figure having the below-listed properties.

- The maximum width is equal to the diameter of two semicircles.
- If the side length of the radius of the semicircle is known, then the overall length of the stadium is equal to 2 * radius + side length.

**4. Mention your observations on Stadium Calculator?**

- Changing the radius affects the overall length, height
- Changing the side length affects the overall length
- The area must be in square units.