Diagonal Of Rectangle Calculator

Background.

The diagonal is the measurement people reach for when the sides alone do not answer the question. A builder setting out a slab measures it to prove the corners are square. Someone moving house uses it to see whether a table top will tilt through a doorway. Television and monitor sizes are quoted by it, which is why a 55-inch widescreen set is only about 48 inches wide.

A diagonal splits the rectangle into two right triangles whose shorter sides are the length and the width, so Pythagoras' theorem gives it directly: square both sides, add them, take the square root. A 3 by 4 rectangle has a diagonal of exactly 5, and that 3-4-5 triangle is the basis of an old setting-out trick. Mark 3 units along one line and 4 along the other; if the marks are 5 apart, the corner is a true right angle. For a whole frame, checking that the two diagonals match does the same job, because a four-sided shape with equal opposite sides and equal diagonals must be a rectangle.

The second number reported is half the diagonal. The diagonals cross at the centre and cut each other in half, so all four corners sit the same distance from that point, on a circle whose diameter is the diagonal. That circle has a practical use: it is the smallest round blank, disc or log end from which the rectangle can be cut.

Length and width may be in any unit, provided both use the same one, and the results come back in that unit. Both sides are needed; an area on its own does not fix the shape, so it cannot fix the diagonal either.

What is diagonal of rectangle calculator?

A diagonal of a rectangle is the straight line joining two opposite corners. Every rectangle has two, they are always equal in length, and they bisect each other at the centre. The length is d = √(l² + w²), which is always longer than the longer side and shorter than the two sides added together. Half of it is the circumradius, the radius of the single circle that passes through all four corners of the rectangle.

How to use this calculator.

1. 01Measure the length and width along two sides that meet at a corner, both in the same unit. If one is in feet and the other in inches, convert before entering.
2. 02Enter them as rectangle length and rectangle width. The order makes no difference, because swapping the sides gives the same diagonal.
3. 03Read the diagonal in your unit. When setting out a frame or slab, measure both diagonals on site and compare each with this figure; if the two site measurements differ, the corners are not square.
4. 04Use the circumcircle radius when you need the smallest circle that holds the rectangle. Double it for the minimum diameter of a round piece to cut the rectangle from.

The formula.

d = √(l² + w²). The diagonal, the length and the width form a right triangle with the diagonal as its hypotenuse, so Pythagoras' theorem applies: the square on the diagonal equals the squares on the two sides added together. The circumradius is R = d ÷ 2, because the diagonals bisect each other at the centre and that point is the same distance from every corner. Squaring lets the longer side dominate. In a 1 by 10 rectangle the diagonal is about 10.05, barely longer than the long side, whereas a square's diagonal is its side times √2, roughly 1.414 times the side. Scaling both sides by the same factor scales the diagonal by that factor, but doubling just one side never doubles it. Both inputs must be greater than zero.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.