Dimensions Of A Rectangle

Find the length and width of a rectangle given its area and perimeter. Free online geometry solver for students, architects, and construction professionals.

Find rectangle dimensions

About This Calculator

The Rectangle Dimensions Calculator finds the length and width of a rectangle when you know its area and perimeter. Given area A and perimeter P, the calculator solves the system L x W = A and 2(L + W) = P using the quadratic formula to return both dimensions.

Frequently Asked Questions

How do you find the dimensions of a rectangle given area and perimeter?

If area = A and perimeter = P, then L = (P/4) + sqrt(P^2 - 16A)/4 and W = (P/4) - sqrt(P^2 - 16A)/4.

What if P^2 - 16A is negative?

No real rectangle exists with the given area and perimeter. The maximum area for a given perimeter is P^2/16 (a square).

What is the relationship between area and perimeter of a rectangle?

For a fixed perimeter, a square maximizes the area. For a fixed area, a square minimizes the perimeter.

Is this calculator free?

Yes, all calculators on Calculy are completely free to use.