Square Diagonal Calculator
Enter the side length of a square and instantly find the diagonal (d = s√2), the area, and the perimeter. Works with any unit — millimetres, centimetres, inches, metres, feet — just stay consistent.
Length of either diagonal of the square (d = s√2)
- 1
Square both legs
10 × 10 = 100The diagonal is the hypotenuse of the 45–45–90 triangle formed by two sides. - 2
Sum of squared legs
100 + 100 = 200 - 3
Diagonal d = √(2s²)
√200 = 14.1421
How does this calculator work?
The diagonal of a square equals the side length multiplied by √2 (≈ 1.4142). Enter the side to get the diagonal, area (s²), and perimeter (4s) instantly. The ratio d/s = √2 is a fixed constant for every square.
Formula
How this is calculated
A square has four equal sides and four right angles. A diagonal connects two opposite corners, splitting the square into two congruent 45–45–90 right triangles. By the Pythagorean theorem on that triangle, the hypotenuse (diagonal) satisfies d² = s² + s², so d = s√2, where √2 ≈ 1.41421356.
This means the diagonal is always about 41.4 % longer than the side — a fixed ratio regardless of the square's size. Area is simply side squared (s²), and perimeter is four times the side (4s).
The formula assumes a perfect (Euclidean) flat square. For real-world measurements, make sure all sides are truly equal and the angles are right angles before relying on the result.
Frequently asked questions
The diagonal of a square with side s is d = s × √2. This comes directly from the Pythagorean theorem applied to the right triangle formed by two sides and the diagonal.
The diagonal is always √2 ≈ 1.4142 times the side length — about 41.4 % longer. This ratio is constant for any square regardless of size.
Yes — rearrange the formula: s = d ÷ √2 (or equivalently s = d × √2 ÷ 2). If the diagonal is 10, the side is 10 ÷ 1.4142 ≈ 7.071.
Also known as
TG we-Calculate Editorial Team. (2026). Square Diagonal Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/square-diagonal-calculator
TG we-Calculate Editorial Team. "Square Diagonal Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/square-diagonal-calculator.
TG we-Calculate Editorial Team, "Square Diagonal Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/square-diagonal-calculator
@misc{wecalculate_square_diagonal_calculator, title = {Square Diagonal Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/square-diagonal-calculator}}, year = {2026}, note = {TG we-Calculate} }
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