Quick answer
The diagonal of a square is d = s√2. A side of 1 gives a diagonal of 1.414214.
Enter the side length. The calculator returns the diagonal.
Related tools: Diagonal of a Rectangle Calculator: Diagonal length of a rectangle. Diagonal Length Calculator: Diagonal of a rectangle or the space diagonal of a box. Square Area Calculator: Area of a square.
How to use the Square Diagonal Calculator
- Enter side (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Side | A number | > 0 |
Formula and method
Formula
d = s√2
IEEE-754 double precision; shown to at most 6 decimal places.
Direct formula.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Side = 1.
| Result | Value |
|---|---|
| Square Diagonal | 1.414214 |
Example 2
Inputs: Side = 10.
| Result | Value |
|---|---|
| Square Diagonal | 14.142136 |
The first line is the headline result (square Diagonal). IEEE-754 double precision; shown to at most 6 decimal places.
Why √2
The diagonal is the hypotenuse of a right triangle with two equal legs of length s, so d = √(s² + s²) = s√2. A 5 m square has a diagonal of 7.07 m.
Practical use
Check that a frame is square by measuring both diagonals: they must be equal, and for a 3 m square equal 4.243 m. A TV is not a square, but a square monitor of diagonal 20 inches has a side of 14.14 inches.
Diagonal and side
The diagonal of a square is the side times √2: a side of 10 gives about 14.1421. It comes from the Pythagorean theorem, s² + s² = d².
To go the other way divide by √2 (or multiply by 0.7071): a diagonal of 10 means a side of about 7.0711. A 12 ft square room is about 16.97 ft corner to corner.
How the result changes with side
Holding every other input at the first worked example, this table changes only side. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Side | Square Diagonal |
|---|---|
| 0.5 | 0.707107 |
| 1 | 1.414214 |
| 2 | 2.828427 |
| 4 | 5.656854 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Side: entering "0" shows "Side must be greater than 0." beside that field and no result.
Choosing between the Square Diagonal Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Diagonal of a Rectangle Calculator](/math/diagonal-of-rectangle/) | length and width | Diagonal |
| [Diagonal Length Calculator](/math/diagonal-length-calculator/) | length and width | Diagonal |
| [Square Area Calculator](/math/square-area-calculator/) | side | Square Area |
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive value
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for side to confirm this.
Frequently asked questions
What side gives a diagonal of 10?
A side of 10 ÷ √2 ≈ 7.071 gives a diagonal of 10.
Is the diagonal always longer than the side?
Yes, by a factor of about 1.414.
Does it work for rectangles?
Use the Diagonal of a Rectangle calculator, d = √(l² + w²).
What is the side of a square with diagonal 10?
10 ÷ √2 ≈ 7.0711.
Why does √2 appear?
Because the diagonal is the hypotenuse of a right triangle with two equal sides, so d = √(s² + s²) = s√2.
What does the Square Diagonal Calculator calculate?
Diagonal of a square. It returns Square Diagonal.
What formula does the Square Diagonal Calculator use?
d = s√2. Direct formula.
What do I need to enter in the square Diagonal Calculator?
You enter Side.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive value.
What is an example of a square Diagonal result?
With side 1, the square Diagonal is 1.414214.
Related calculators
- Diagonal of a Rectangle Calculator — Diagonal length of a rectangle.
- Diagonal Length Calculator — Diagonal of a rectangle or the space diagonal of a box.
- Square Area Calculator — Area of a square.
- Area Calculator — Area of common two-dimensional shapes.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Pythagorean Theorem Calculator — Find the hypotenuse or a missing leg of a right triangle.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.