Square Diagonal Calculator
Find the diagonal of a square from its side, the side from its diagonal, or the area straight from the diagonal — with a live diagram and show-your-work steps.
Diagonal
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Side
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Diagonal
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Area
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Perimeter
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Show your work
The diagonal splits the square into two identical right triangles — that is why d = s√2.
Worked examples
Tap one to load it into the calculator.
Scope boundary — what this tool is (and is not)
- This tool: the diagonal of a square — all four sides equal. Formula d = s√2.
- Cube space diagonal (3D): runs through the body of a cube, d = s√3 — see our cuboid surface area calculator (includes the space diagonal).
- Any right triangle: legs may differ — use the hypotenuse calculator.
- Golden rectangle: diagonal follows a different rule, d = a√(1+φ²) — see the golden rectangle solver.
- TV / monitor screens: screen diagonals depend on the aspect ratio (16:9, …) — see the TV size viewing lab.
Frequently asked questions
What is the formula for the diagonal of a square?
The diagonal of a square is d = s × √2, where s is the side length. For example, a square with side 10 cm has a diagonal of 10 × √2 = 14.142135623730951 cm.
How do I find the side of a square from its diagonal?
Divide the diagonal by √2: s = d ÷ √2. A square with a 10 cm diagonal has a side of 10 ÷ √2 = 7.0710678118654755 cm.
How do I find the area of a square from its diagonal?
Use A = d² ÷ 2. A square with a 10 cm diagonal has an area of 10² ÷ 2 = 50 cm² — you never need to find the side first.
What is the diagonal of a 5 by 5 square?
Multiply the side by √2: 5 × √2 = 7.0710678118654755.
Is the diagonal of a square always longer than its side?
Yes. The diagonal is √2 ≈ 1.4142135623730951 times longer than the side, for every square.
What is the difference between a square diagonal and a cube diagonal?
A square diagonal runs across one flat face: d = s√2 ≈ 1.4142 × s. A cube's space diagonal passes through the solid body: d = s√3 ≈ 1.7321 × s. They are different lines — do not mix the two formulas up.
Can I use the Pythagorean theorem to find a square's diagonal?
Yes — the diagonal is the hypotenuse of a right triangle whose legs both equal the side: d = √(s² + s²) = √(2s²) = s√2.
What is the diagonal of a square with a 12-inch side?
12 × √2 = 16.97056274847714 inches (about 16.97 in).
Free tool by NRTechStudio