Square Diagonal Calculator
Calculate the diagonal of a square from the side length, or find the side length from the diagonal. This calculator also shows the area and perimeter of the square.
The diagonal of a square connects two opposite corners and is always longer than the sides. The relationship comes directly from the Pythagorean theorem.
The Formula:
d = s x sqrt(2)
Since a square's diagonal splits it into two right triangles with legs of length s, the diagonal is the hypotenuse: d = sqrt(s² + s²) = s x sqrt(2).
Working Backwards:
If you know the diagonal, the side length is s = d / sqrt(2), which equals d x sqrt(2) / 2.
Area from the Diagonal:
You can also find a square's area directly from its diagonal: A = d²/2. This works because A = s² and s = d/sqrt(2), so A = d²/2.
Where This Comes Up:
Square diagonals matter in construction (measuring if a frame is square), screen sizes (TV and monitor diagonals), woodworking (cutting diagonal braces), and even baseball (the distance between home plate and second base on a 90-foot diamond is 90 x sqrt(2) = about 127.3 feet).