Mathematical Calculators

Diagonal of a rectangle

Use this simple calculator to determine the diagonal of any rectangle. Works with all units.

Diagonal of Rectangle Calculator

Table of contents

◦What is the diagonal of a rectangle?
◦How to use this calculator
◦Related rectangle formulas
◦Properties of a rectangle's diagonals
◦Why diagonals matter
◦FAQ

What is the diagonal of a rectangle?

The diagonal of a rectangle is the straight line connecting two opposite corners. For a rectangle with length l and width w, the diagonal d is given by the Pythagorean theorem:

d = √(l² + w²)

This works because the diagonal forms the hypotenuse of a right triangle whose other two sides are the length and width of the rectangle.

How to use this calculator

  1. Enter the length of the rectangle in any unit (cm, in, m, ft — the result will be in the same unit).
  2. Enter the width in the same unit.
  3. The diagonal is calculated automatically.

For a 3 × 4 rectangle, the diagonal is √(9 + 16) = √25 = 5.

If you have other measurements of the rectangle, you can derive the diagonal in several ways:

  • Length and width (the standard case): d = √(l² + w²)
  • Length and area: d = √(l² + (A/l)²)
  • Width and area: d = √(w² + (A/w)²)
  • Length and perimeter: d = √(2l² − P·l + P²/4)
  • Width and perimeter: d = √(2w² − P·w + P²/4)
  • Area and angle (α between diagonals): d = √(2A / sin α)
  • Circumscribed circle radius (r): d = 2r

Properties of a rectangle's diagonals

A rectangle has two diagonals, and they share a few useful properties:

  • They are always equal in length (unlike a general parallelogram).
  • They bisect each other — they cross at the rectangle's center, and each diagonal is cut into two equal halves at that point.
  • They do not generally meet at right angles. They only meet at 90° when the rectangle is a square.
  • The point where they intersect is the circumcenter — the center of the unique circle that passes through all four vertices.

Why diagonals matter

Diagonals show up in a lot of practical problems: measuring whether a piece of furniture fits through a doorway, finding the screen size of a TV from its width and height, packing rectangular objects in a box, or laying out a rectangular plot of land.

If you know any two of {length, width, diagonal}, the third is fully determined — that's just the Pythagorean theorem rearranged.

FAQ

Do the diagonals of a rectangle intersect at 90°?

Only if the rectangle is a square. In any other rectangle the diagonals cross at the center but at an angle other than 90°. The angle depends on the ratio of length to width — as the rectangle gets narrower, the angle gets sharper.

Are the two diagonals always the same length?

Yes. In every rectangle, the two diagonals are equal. This is what distinguishes rectangles from non-rectangular parallelograms, which have diagonals of different lengths.

Can I get a side from the diagonal?

If you know the diagonal and one side, yes — the Pythagorean theorem gives you the other side: w = √(d² − l²). If you only know the diagonal, you have one equation in two unknowns and need a second measurement (area, perimeter, or angle).