Diagonal of a Square Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Nov 20, 2022

Find out the length of the square's diagonal with our diagonal of a square calculator. Check out below how to find the diagonal of a square formula, or simply give our tool a try - you won't be disappointed.

Diagonal of square

diagonals of the square with side a

A diagonal is a line segment that joins two non-neighboring vertices. Each quadrilateral has two diagonals, a square too. Its diagonals are:

  • Equal in length;
  • Perpendicular bisectors of each other; and
  • Bisectors of square angles.

Each diagonal divides the square into two congruent isosceles right triangles — we made the 45 45 90 triangle calculator about them. Such a triangle has half of the area of a square, its legs are square sides, and the hypotenuse equals the length of the diagonal of a square.

How to find the diagonal of a square - formula

To calculate the diagonal of a square, multiply the length of the side by the square root of 22:

d=a2d = a\cdot\sqrt{2}

So, for example, if the square side is equal to 5 in, then the diagonal is 52 in7.071 in5\sqrt{2}\ \text{in} \approx 7.071\ \text{in}. Type that value into the diagonal of a square calculator to check it yourself!

Where does this equation come from? You can derive this diagonal of square formula e.g., from calculating the Pythagorean theorem.

  1. As we noticed before, the diagonal of a square divides the square into two congruent right triangles.
  2. Legs are square sides, and the length of the diagonal of the square is the hypotenuse. Given the side length of the square:
a2+a2=diagonal2diagonal=a2+a2=2a2diagonal=a2\begin{split} &a^2+a^2=\text{diagonal}^2\\ &\text{diagonal} = \sqrt{a^2+a^2}=\sqrt{2\cdot a^2}\\ &\text{diagonal}=a\cdot\sqrt{2} \end{split}

This is the same as calculating the hypotenuse in a right triangle.

If you don't have the side of a square given, use other formulas:

d=2aread = \sqrt{2\cdot\text{area}}

If the area is given, and:

d=perimeter42d = \frac{\text{perimeter}}{4}\cdot\sqrt{2}

If we know the square's perimeter.

🙋 We can also teach you how to find the diagonal of a rectangle with our diagonal of a rectangle calculator!

How to find the length of diagonal of square?

With our calculator, it's a piece of cake!

  1. Type the given value into a proper box. Let's say we know that the square side is equal to 8 in.
  2. Diagonal of a square calculator displays the result! In our case, the diagonal is 15.556 in15.556\ \text{in}.
  3. If you want to check the result in a different unit, click on the unit name and select the one that meets your needs. For instance, 15.556 in15.556\ \text{in} is 39.51 cm39.51\ \text{cm} and around 1 ft 3 in1\ \text{ft}\ 3\ \text{in}.
  4. The diagonal of a square calculator works the other way round as well - knowing the diagonal, you can calculate the square side.

Now you're the expert, and you know exactly how to find the diagonal of a square given square sides. However, if you don't have it provided, use this general square calculator, where you can type the area or perimeter, and the tool will also find the diagonal.

Hanna Pamuła, PhD
Image of a square with side a and diagonal d. Diagonal of a square
Side a
in
Diagonal d
in
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