Diagonal of a Square
Length of the diagonal of a square.
Formula
Variables
Example
A square of side 5 has diagonal d = 5√2 ≈ 7.07.
How it works
In a square, the diagonal joins opposite corners and splits the square into two right triangles. Each triangle has two equal legs of length a, so by Pythagoras the diagonal is d = \u221a(a^2 + a^2) = a\u221a2. This is why the diagonal is always about 1.414 times the side length.
When to use it
Use this when you know the side of a square and need the corner-to-corner distance. It is common in geometry problems, design/layout work, tiling, and checking measurements across a square shape.
Worked example, step by step
A square has side length 12 cm. Use d = a\u221a2 Substitute a = 12: d = 12\u221a2 Compute: d \u2248 12 \u00d7 1.414 = 16.97 Final answer: the diagonal is about 16.97 cm
Common mistakes to avoid
- Using d = 2a instead of the Pythagorean theorem
- Forgetting that the diagonal is longer than the side but shorter than the perimeter
- Rounding \u221a2 too early and losing accuracy
Did You Know?
A square's diagonal is √2 times its side — the very number the ancient Greeks proved was irrational.
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