A square’s diagonal length, computed directly from its side length.
How it works
Multiplying the side length by the square root of 2 gives the diagonal, a direct application of the Pythagorean theorem to the square’s two equal sides.
What this does not include
This does not include rectangles with unequal sides — for those, use this site’s rectangle calculator instead, which handles a separately known length and width.
How to use this calculator
- Enter the side length.
A worked example
A square with side 5: diagonal = side × √2 = 7.0711.
Side 10: diagonal = 14.1421.
What the variables mean
| Variable | Meaning |
|---|---|
| Side length | Length of each of the square’s four equal sides |
Edge cases worth knowing
The diagonal is always side × √2, a direct application of the Pythagorean theorem to a right triangle formed by two sides and the diagonal.
The diagonal scales linearly with side length, unlike area — doubling the side length exactly doubles the diagonal, but quadruples the area.
Frequently asked questions
Why does the diagonal always equal side times the square root of 2?
A square’s diagonal forms the hypotenuse of a right triangle whose two legs are both the side length — the Pythagorean theorem then gives exactly this relationship.
What’s a practical use for checking a diagonal?
Confirming that a square frame, tile, or foundation is actually square — if the measured diagonal doesn’t match this calculated value, the corners aren’t true right angles.
Is the diagonal always longer than the side?
Yes — since the square root of 2 is about 1.41, the diagonal is always roughly 41% longer than the side.
