Perimeter of a Rectangle Calculator

Published on: June 9, 2024
Final Answer: Free • Full Steps: Plus

This Perimeter of a Rectangle Calculator finds the distance all the way around a rectangle from its width and its length, and shows the working line by line. A rectangle has two lengths and two widths, so one length plus one width covers half of the journey around it, and doubling that total covers the rest. The answer is written in units. Following the same pattern every time is what makes the perimeter of a rectangle easy to picture, check, and work out on your own.

Rectangle with sides labeled w and l

In the diagram, the width is \(w\) and the length is \(l\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the length and the width into the formula.
  4. Add the length and the width inside the brackets.
  5. Double that total to get the perimeter.

Formula:

\(P = 2(l + w)\)
See Example 1 Hide Example 1

Problem

\(w = 8, l = 6\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the length and the width into the formula.
  4. Add the length and the width inside the brackets.
  5. Double that total to get the perimeter.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the perimeter of a rectangle whose width is \(w = 8\) and whose length is \(l = 6\).

\(w = 8,\; l = 6\)

Step 2

Step 2 - Write the formula.

In this problem: A rectangle has two lengths and two widths, so one length plus one width covers half of the way around, and doubling that covers the whole perimeter.

\(P = 2(l + w)\)

Step 3

Step 3 - Substitute the length and the width into the formula.

In this problem: Replacing \(l\) with \(6\) and \(w\) with \(8\) in \(P = 2(l + w)\) gives \(P = 2(6 + 8)\).

\(P = 2(6 + 8)\)

Step 4

Step 4 - Add the length and the width inside the brackets.

In this problem: Adding the length and the width gives \(6 + 8 = 14\).

\(P = 2(14)\)

Step 5

Step 5 - Double that total to get the perimeter.

In this problem: Doubling that total gives \(2 \times 14 = 28\).

\(P = 2(14) = 28\)

Final Answer

\(P = 28\)
See Example 2 Hide Example 2

Problem

\(w = 2.5, l = 4\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the length and the width into the formula.
  4. Add the length and the width inside the brackets.
  5. Double that total to get the perimeter.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the perimeter of a rectangle whose width is \(w = 2.5\) and whose length is \(l = 4\).

\(w = 2.5,\; l = 4\)

Step 2

Step 2 - Write the formula.

In this problem: A rectangle has two lengths and two widths, so one length plus one width covers half of the way around, and doubling that covers the whole perimeter.

\(P = 2(l + w)\)

Step 3

Step 3 - Substitute the length and the width into the formula.

In this problem: Replacing \(l\) with \(4\) and \(w\) with \(2.5\) in \(P = 2(l + w)\) gives \(P = 2(4 + 2.5)\).

\(P = 2(4 + 2.5)\)

Step 4

Step 4 - Add the length and the width inside the brackets.

In this problem: Adding the length and the width gives \(4 + 2.5 = 6.5\).

\(P = 2(6.5)\)

Step 5

Step 5 - Double that total to get the perimeter.

In this problem: Doubling that total gives \(2 \times 6.5 = 13\).

\(P = 2(6.5) = 13\)

Final Answer

\(P = 13\)

Example Problems

Click one to load it into the box and solve it.