Width of a Rectangle Calculator

Enter a rectangle's length plus its area, perimeter, or diagonal to solve for the width, using the matching geometric formula.

Quick Facts

From area & length
w = A / l
Divide the area by the length to get the width.
From perimeter & length
w = P / 2 - l
Half the perimeter equals length plus width.
From diagonal & length
w = √(d² - l²)
Follows from the Pythagorean theorem: l² + w² = d².

Your Results

Calculated
Width
-
Solved from your inputs
Area
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A = length × width
Perimeter
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P = 2(length + width)
Diagonal
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d = √(length² + width²)

Ready

Enter the length and one known quantity, then press Calculate.

Formula and Method for the Width of a Rectangle

A rectangle has two pairs of equal, parallel sides: the length (the longer side, by convention) and the width (the shorter side). You often know the length plus one other measurement — the area, the perimeter, or the diagonal — and need to back out the width. This calculator solves for width using whichever of those three relationships matches what you already know, then reports the width alongside the full set of area, perimeter, and diagonal.

How the calculation works

Each method rearranges a standard rectangle formula to isolate width (w), given the length (l):

  • From area: since A = l × w, width is w = A / l.
  • From perimeter: since P = 2(l + w), half the perimeter is l + w, so width is w = P / 2 - l.
  • From diagonal: the diagonal splits a rectangle into two right triangles with legs l and w, so by the Pythagorean theorem l² + w² = d², giving width w = √(d² - l²).

Once the width is known, the calculator fills in the remaining values: area (l × w), perimeter (2(l + w)), and diagonal (√(l² + w²)). Enter the length and known quantity in the same unit system — mixing feet and inches, or centimeters and meters, produces incorrect results.

Common mistakes

  • Entering area in the wrong units: if the length is in feet, the area must be in square feet (ft²), not square inches or square meters.
  • Perimeter smaller than twice the length: since w = P/2 - l must be positive, the perimeter has to be greater than 2 × length, otherwise the shape is not a valid rectangle.
  • Diagonal shorter than the length: the diagonal is always the longest measurement in a rectangle, so it must be greater than the length — if it is not, the inputs are inconsistent.

Real-world applications

  • Construction and carpentry, where you know a room's length and its floor area from a permit or blueprint and need the missing wall width.
  • Framing and fencing, where you know the total perimeter of material available and one side, and need the other.
  • Furniture and screen sizing, where you know a diagonal (a TV's advertised size) and one side, and need the other.
  • Land surveying and landscaping, converting between area, perimeter, and side lengths for irregular-shaped lots approximated as rectangles.

Frequently Asked Questions

How do you find the width of a rectangle if you know the area and length?
Divide the area by the length: w = A / l. For example, a rectangle with an area of 48 ft² and a length of 8 ft has a width of 48 / 8 = 6 ft.
How do you find the width if you know the perimeter and length?
Halve the perimeter, then subtract the length: w = P / 2 - l. A rectangle with a 30 ft perimeter and an 8 ft length has a width of 30 / 2 - 8 = 7 ft.
How do you find the width if you know the diagonal and length?
Use the Pythagorean theorem: w = √(d² - l²), since the diagonal is the hypotenuse of the right triangle formed by the length and width. A rectangle with a 10 ft diagonal and an 8 ft length has a width of √(10² - 8²) = √36 = 6 ft.
What is the difference between length and width?
By convention, length refers to the longer side of a rectangle and width (or breadth) to the shorter side, though the labels are arbitrary as long as you stay consistent — swapping them does not change the area, perimeter, or diagonal.

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