How to Find the Perimeter of a Rectangle

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The perimeter of a rectangle is the sum total length of all of its sides. [1] A rectangle is defined as a quadrilateral, or a geometric shape with four sides. In a rectangle, both sets of opposite sides are congruent, meaning that they are the same length. [2] While not all rectangles are squares, all squares can be considered rectangles, and a compound shape may be composed of rectangles. [3]

Method 1
Method 1 of 4:

Finding Perimeter with Length and Width

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  1. This formula will help guide you as you calculate the perimeter of your own rectangle. The basic formula is: P = 2 * (l + w) . [4]
    • Perimeter is always the total distance around the outside edge of any shape, whether it is simple or compound.
    • In this equation, P stands for “perimeter,” l refers to the length of the rectangle, and w refers to the width of the rectangle.
    • Length always has a greater value than width.
    • Because opposite sides of a rectangle are equal, both lengths will be the same and both widths will be the same. This is why you write the equation as a multiplication of the sum of the length and width by 2.
    • You can also write the equation as P = l + l + w + w to make this very clear.
  2. For a basic math problem at school, the length and width of the rectangle will be provided in the problem. These are usually next to the figure of the rectangle. [5]
    • If you are calculating the perimeter of a rectangle in real life, use a ruler, yardstick, or tape measure to find the length and width of the area that you are trying to measure. If you’re measuring outdoors, measure all sides to see if the opposites are truly congruent.
    • For example, l = 14 centimeter (5.5 in), w = 8 centimeter (3.1 in).
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  3. [6] After you identify your length and width, you want to plug them into the “l” and “w” slots in the perimeter equation.
    • When you are working out your perimeter equations, note that according to the order of operations, mathematical expressions contained inside brackets or parentheses are solved before those outside of the parentheses. [7] So, you’ll begin solving your equation by adding the length and width.
    • For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22).
  4. When you’re looking the formula for the perimeter of a rectangle, the “(l + w)” is multiplied by two. Once you’ve completed this multiplication, you have the perimeter of your rectangle. [8]
    • This multiplication takes into account the other two sides of your rectangle. When you added together the width and length, you only added together two sides of the shape.
    • Since the other two sides of the rectangle are equal to the two already added together, you can simply multiply this measurement by two in order to find the total sum of all four sides.
    • For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in) .
  5. Instead of adding two sides of your rectangle and multiplying by two, you can simply add all four sides together directly to find the perimeter of your rectangle. [9]
    • If you struggle with the concept of perimeter, this is a great place to start.
    • For example, P = l + l + w + w = 14 + 14 + 8 + 8 = 44 centimeter (17.3 in) .
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Method 2
Method 2 of 4:

Calculating the Perimeter with Area and One Side

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  1. Even though you already know the area of the rectangle in this problem, you will still need to use the area formula to find missing information.
    • The area of a rectangle is a measurement of the two-dimensional space within the rectangle, or the number of square units within the rectangle.
    • The formula used to find the area of a rectangle is A = l * w .
    • The formula used to find the perimeter of a rectangle is P = 2 * (l + w)
    • In the above formulas, A stands for “area,” P stands for “perimeter,” l refers to the length of the rectangle, and w refers to the width of the rectangle.
  2. This will allow you to find the measurement of the missing side of your rectangle, whether it is the length or the width. Finding this missing piece of information will then allow you to calculate perimeter.
    • Because you multiply the length and width together to find the area, dividing the area by the width will give you the length. Likewise, dividing the area by the length will give you the width.
    • For example, A = 112 centimeter (44.1 in) squared, l = 14 centimeter (5.5 in)
      • A = l * w
      • 112 = 14 * w
      • 112/14 = w
      • 8 = w
  3. Now that you have measurements for both the length and width, you can plug them into the formula for rectangular perimeter. [10]
    • In this problem, you add length and width together first because this part of the equation occurs in parentheses.
    • According to the order of operations, you always do the part of the equation in parentheses first.
  4. Once you’ve added the length and width of your rectangle together, you can find its perimeter by multiplying by two. This takes into account the additional two sides of your rectangle. [11]
    • You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length.
    • Both lengths of the rectangle are the same, and both widths are the same.
    • For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).
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Method 3
Method 3 of 4:

Figuring Out the Perimeter of a Compound Rectangle

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  1. [12] Perimeter is the sum total of all outer sides of any given shape, including irregular and compound shapes.
    • A standard rectangle has four sides. The two sides composing the length are equal to each other, and the two sides composing the width are equal to each other. Therefore, the perimeter is the sum of those four sides.
    • A compound rectangle has at least six sides. Think of a capital “L” or “T” shape. The top “branch” can be separated into one rectangle and the bottom “bar” can be separated into another. The perimeter of this shape, however, does not rely on breaking up the compound rectangle into two separate rectangles. Instead, the perimeter is simply: P = s1 + s2 + s3 + s4 + s5 + s6 .
    • Each “s” represents a different side of your compound rectangle.
  2. In a standard educational math problem, the measurement of all sides should be provided. [13]
    • This example uses the abbreviations L, W, l1, l2, w1, and w2. The uppercase L and W stand for the full lengths and widths of the shape. The lowercase l s and w s stand for the smaller lengths and widths.
    • As such, the formula P = s1 + s2 + s3 + s4 + s5 + s6 equals P = L + W + l1 + l2 + w1 + w2 .
    • Variables, like “w” or “l” are simply placeholders for unknown numeric values. [14]
    • Example: L = 14 centimeter (5.5 in), W = 10 centimeter (3.9 in), l1 = 5 centimeter (2.0 in), l2 = 9 centimeter (3.5 in), w1 = 4 centimeter (1.6 in), w2 = 6 centimeter (2.4 in)
      • Note that l1 and l2 will equal L . Similarly, w1 and w2 will equal W .
  3. By plugging the numeric values of the sides into your equations, you’ll be able to find the perimeter of your compound shape. [15]
    • P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 centimeter (18.9 in)
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Method 4
Method 4 of 4:

Measuring the Perimeter of a Compound Rectangle with Limited Information

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  1. You can still find the perimeter of a compound rectangle as long as you have at least one full length or full width and at least three of the minor width or length measurements.
    • For an “L”-shaped compound rectangle, use the formula P = L + W + l1 + l2 + w1 + w2
    • In this formula, P stands for “perimeter.” The uppercase L and W stand for the full lengths and widths of the entire compound shape. The lowercase l s and w s stand for the smaller lengths and widths in the compound shape.
    • Example: L = 14 centimeter (5.5 in), l1 = 5 centimeter (2.0 in), w1 = 4 centimeter (1.6 in), w2 = 6 centimeter (2.4 in); missing: W, l2
  2. In this example, the full length, L , will be equal to the sum of l1 and l2 . Likewise, the full width, W , will be equal to the sum of w1 and w2 . Using this knowledge, add and subtract the measurements you do have to find the two missing measurements.
    • Example: L = l1 + l2; W = w1 + w2
      • L = l1 + l2
      • 14 = 5 + l2
      • 14 – 5 = l2
      • 9 = l2
      • W = w1 + w2
      • W = 4 + 6
      • W = 10
  3. Once you have subtracted to find your missing measurements, you can add all of your sides together to find the perimeter of the compound rectangle. Now, you’ll use the original perimeter formula. [16]
    • P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 centimeter (18.9 in)
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Calculator, Practice Problems, and Answers

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  • Question
    How do I compute the missing side of a triangle?
    Taylor Klein
    Advanced Math Teacher
    Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration.
    Taylor Klein
    Advanced Math Teacher
    Expert Answer
    When dealing with a rectangle, you can find the length of the missing side by utilizing division or by manipulating the equation through your understanding of literal equations. In the context of triangles, a similar principle applies. If you know the area and the lengths of two sides of a triangle, you can employ appropriate formulas, such as the formula for the area of a triangle. To solve for the length of the missing side, the Pythagorean theorem is commonly used for right-angled triangles, and trigonometric ratios can be employed for various types of triangles. It ultimately depends on the specifics of the triangle in question.
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    Not Helpful 4 Helpful 1
  • Question
    How can I find the side of a rectangle if perimeter is given?
    Donagan
    Top Answerer
    You can't. With any given perimeter, an infinite number of length-width combinations would be possible.
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  • Question
    How do I find the perimeter with difficult shapes?
    Community Answer
    It can help to break difficult shapes up into simpler shapes. Use area formulas for these simpler shapes to help you find all the side lengths of the complex shape.
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      References

      1. ↑ https://www.mathsisfun.com/geometry/perimeter.html
      2. ↑ https://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/rectangles_rhombuses_squares
      3. ↑ https://www.cimt.org.uk/projects/mepres/book7/bk7i9/bk7_9i4.htm
      4. ↑ http://www.mathopenref.com/rectangleperimeter.html
      5. ↑ https://www.cuemath.com/measurement/perimeter-of-a-rectangle/
      6. ↑ https://www.cuemath.com/measurement/perimeter-of-a-rectangle/
      7. ↑ http://www.algebrahelp.com/lessons/simplifying/oops/
      8. ↑ https://www.omnicalculator.com/math/perimeter-of-rectangle
      9. ↑ https://www.omnicalculator.com/math/perimeter-of-rectangle
      1. ↑ https://www.cuemath.com/measurement/perimeter-of-a-rectangle/
      2. ↑ https://www.omnicalculator.com/math/perimeter-of-rectangle
      3. ↑ https://www.thatquiz.org/tq/previewtest?1/6/A/A/RBLR1385390054
      4. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-geometry-for-ccss/section/1.9/primary/lesson/composite-shapes-geo-ccss/
      5. ↑ https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variables-and-expressions/v/what-is-a-variable
      6. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-geometry-for-ccss/section/1.9/primary/lesson/composite-shapes-geo-ccss/
      7. ↑ https://www.cuemath.com/measurement/area-of-composite-shapes/

      About This Article

      Article Summary X

      To find the perimeter of a rectangle, use the formula P = 2 × (l + w). First, find the length and width of the rectangle, and place them in the “l” and “w” variables in the equation. Then, add these measurements together. For example, for a rectangle with a length of 14 cm and a width of 8 cm, you would add them to get 22 cm. Multiply the sum of the numbers by 2 to get the perimeter, which in this case would be 44 cm. Be sure to label your answer with the proper units! If you need to find the perimeter of a rectangle if you only know the area and the length of one side, keep reading the article!

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