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Square Diagonal

Also known as diagonal of a square · corner to corner square · s root 2

d=s2d = s\sqrt{2}

Worked example: unit square → diagonal sqrt(2) m — press Try an example to run it live, then adjust anything.

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Square Diagonal explained

ds

Cut a square corner to corner and you get two right triangles whose legs are both ss, so Pythagoras gives d=s2≈1.414sd = s\sqrt{2} \approx 1.414s. Carpenters use this constantly in reverse: to check that a frame is square, measure both diagonals — if they match, the corners are true. It also sets the largest square that fits through a doorway, and the reach of a diagonal brace.

The number 2\sqrt{2} itself has a claim to fame: it was the first quantity proved irrational, around the 5th century BC, precisely because it is the diagonal of the unit square. Paper sizes exploit it too — A4 and its siblings have a 2\sqrt{2} aspect ratio, which is why folding one in half yields the same proportions again.

Square Diagonal formula

d=s2d = s\sqrt{2}
Where
  • dd= Diagonal (m)
  • ss= Side length (m)

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