Diagonal of a Rectangle Calculator

This calculator works out the diagonal length of any rectangle using the Pythagorean theorem, along with perimeter, area and the angle the diagonal makes with each side. It suits any time you need the straight-line distance between two opposite corners of a rectangular space or object, whether that is checking a deck or garden bed is truly square, sizing a screen or box, or working through a geometry problem. You enter the length and width of the rectangle and choose a unit from millimetres, centimetres, metres, inches or feet, and the calculator instantly returns the diagonal length, perimeter and area in that unit, plus the angle the diagonal forms with the length side. A breakdown shows every step: the length and width squared, the sum of those squares, and the square root that gives the diagonal, alongside the angle between the diagonal and each side and confirmation that both diagonals of a rectangle are always equal. The default 8 m by 6 m example demonstrates the classic 3-4-5 triangle, giving a clean 10 m diagonal. Because a rectangle's diagonals must match for its corners to be true right angles, this tool doubles as a way to check whether something you are building is properly square: measure both diagonals and see if they agree. Results are rounded for display, so use more decimal places for construction or engineering precision.

Rectangle Results

Diagonal Length
10.00
m

Perimeter

28.00 m

Sum of all 4 sides

Area

48.00 m2

Length × width

Diagonal Angle

36.9°

From the length side

How to Find the Diagonal of a Rectangle

A rectangle has two diagonals, each connecting a pair of opposite corners. Because a rectangle has four right angles, drawing a diagonal splits it into two right-angled triangles. The diagonal itself becomes the hypotenuse of each triangle, while the length and width form the two shorter sides. This means the Pythagorean theorem applies directly: the diagonal squared equals the length squared plus the width squared.

The Formula

The diagonal (d) of a rectangle with length (l) and width (w) is:

d = √(l² + w²)

For example, a rectangle with a length of 8 m and a width of 6 m has a diagonal of √(8² + 6²) = √(64 + 36) = √100 = 10 m. This is a well-known "3-4-5 triangle" scaled up, which is why it gives a whole number result.

Step	Calculation	Result
Square the length	8²	64
Square the width	6²	36
Add the squares	64 + 36	100
Take the square root	√100	10 m

Step

Calculation

Result

Square the length

8²

Square the width

6²

Add the squares

64 + 36

100

Take the square root

√100

10 m

Finding a Missing Side from the Diagonal

If you already know the diagonal and one side, you can rearrange the formula to find the missing side: missing side = √(d² minus known side²). This is useful when measuring a space where the diagonal is easier to check than a single side, such as confirming a door frame, deck, or garden bed is square (a true rectangle has equal diagonals, so if both diagonals match, the corners are 90 degrees).

Where This Is Used

Checking that a building frame, deck, or garden bed is square by comparing the two diagonals

Working out the screen size (diagonal) of a TV, monitor or phone from its width and height

Finding the longest straight object that will fit flat inside a rectangular box or room

Geometry and trigonometry study, including angle and triangle problems

Related Calculators

Maths and Stats Calculators: the full hub of maths tools.

Area of a Rectangle Calculator: work out area from length and width.

Diagonal of a Square Calculator: the special case where all sides are equal.

Pythagorean Theorem Calculator: the underlying formula for any right-angled triangle.

Perimeter Calculator: work out the perimeter of common shapes.

Sources: Pythagorean theorem, standard Euclidean geometry (rectangle diagonal = hypotenuse of two congruent right-angled triangles formed by the length and width).

This calculator applies standard geometry and works with any consistent unit of measurement. Results are rounded for display; use more decimal places for engineering or construction precision.

Frequently asked questions

What is the formula for the diagonal of a rectangle?

The diagonal of a rectangle is found using the Pythagorean theorem: diagonal = square root of (length squared plus width squared), written as d = sqrt(l^2 + w^2). This works because a rectangle's diagonal splits it into two right-angled triangles, with the diagonal as the hypotenuse and the length and width as the two shorter sides.

Do both diagonals of a rectangle have the same length?

Yes. A rectangle has two diagonals and they are always equal in length, because opposite sides of a rectangle are equal and each diagonal forms a right-angled triangle with the same pair of side lengths. This is one of the defining properties of a rectangle, and it is also true for squares since a square is a special rectangle.

How do I find the length or width if I know the diagonal?

Rearrange the Pythagorean theorem. If you know the diagonal (d) and one side, the other side is found using: missing side = square root of (d^2 minus known side^2). For example, if the diagonal is 5 m and the length is 4 m, the width is the square root of (25 minus 16), which is 3 m.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland by SiteHost New Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-08-19 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.

Diagonal of a Rectangle Calculator

1. Rectangle Dimensions

2. About the Diagonal