Length And Width Of Rectangle Given Perimeter
Find the missing side (width) of a rectangle when you know the perimeter and length. Uses formula W = P/2 - L. Get area, diagonal, and instant results.
About This Calculator
The Length And Width Of Rectangle Given Perimeter Calculator helps you find the missing dimension of any rectangle when you know its perimeter and one side. This is a fundamental geometry tool for students, teachers, architects, construction professionals, and DIY enthusiasts who need to determine unknown rectangle dimensions quickly and accurately.
The calculator uses the standard rectangle perimeter formula P = 2(L + W), rearranged to solve for the unknown side. If you know the perimeter P and the length L, the width is calculated as W = P/2 - L. Once both sides are known, the tool automatically computes the area (L x W) and the diagonal (sqrt(L^2 + W^2)) using the Pythagorean theorem. This complete set of results gives you a full geometric picture of the rectangle.
The underlying math is simple. The perimeter is the total distance around the rectangle: P = 2L + 2W. Dividing both sides by 2 gives P/2 = L + W. Subtracting the known length yields width = P/2 - L. This formula works for any unit of measurement -- inches, feet, centimeters, meters, yards, or any other linear unit -- as long as all measurements use the same unit.
Why you need one known side: A rectangle with only the perimeter specified has infinitely many possible dimension pairs. For example, a rectangle with a perimeter of 20 units could be 1x9, 2x8, 3x7, 4x6, 5x5, or any other pair summing to 10. To find a specific pair, you must know either the length or the width. This is why the calculator requires both inputs.
Applications
Construction & Renovation: Builders often know the perimeter of a room (from baseboard measurements) and one wall length, needing to find the other wall to order materials like flooring, tiles, or paint.
Gardening & Landscaping: Gardeners planning a rectangular flower bed or vegetable patch may know the fencing material (perimeter) and the desired length, needing to calculate the width to ensure proper spacing.
Education: Students learning geometry can verify their homework by entering known values and checking the computed results against their manual calculations.
Interior Design: When arranging furniture in a rectangular room, knowing two adjacent wall lengths helps determine available floor area and diagonal clearance.
Frequently Asked Questions
How do I find the width of a rectangle given the perimeter and length?
Use the formula W = P/2 - L, where P is the perimeter and L is the length. For example, if the perimeter is 20 units and the length is 6 units, the width is 20/2 - 6 = 4 units.
Can I find both length and width with only the perimeter?
No -- a rectangle has infinitely many length-width pairs that satisfy a given perimeter (any L + W = P/2). You need at least one side to determine the other uniquely.
What does the formula P = 2(L + W) mean?
The perimeter of a rectangle equals twice the sum of its length and width. Rearranging gives L + W = P/2, so if you know either side you can solve for the missing one.
What are the area and diagonal of the rectangle?
Once both length and width are known, the area is L x W and the diagonal is sqrt(L^2 + W^2) using the Pythagorean theorem. Both are shown in the results.
What if my length is greater than or equal to half the perimeter?
A valid rectangle must have length less than P/2. If length >= P/2, the width becomes zero or negative, which is impossible. Enter a smaller length value.
What units should I use for perimeter and length?
Any consistent linear unit -- inches, feet, centimeters, meters, yards, or miles. Both inputs must use the same unit for the results to be accurate. The results will be in the same unit.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use. No registration, no downloads, and no hidden fees.
Can this calculator help me with irregular shapes?
No -- this calculator only works for rectangles. For irregular quadrilaterals or other shapes, you would need different formulas or a more general polygon calculator.