How this calculator works
Each diagonal is the hypotenuse of a right triangle. The diagonals bisect each other, and all corners lie on a circle whose radius is half the diagonal. For a long thin rectangle the acute crossing angle is small; for a square both crossing angles are 90°. Diagonal-and-angle mode recovers both sides using half that crossing angle.
Formula
d = hypot(l,w); r = d/2; acute angle α = 2 atan(w/l), with l ≥ w. Conversely l = d cos(α/2), w = d sin(α/2).
Worked example
A 4 m by 3 m rectangle has diagonal 5 m and circumradius 2.5 m. Its acute crossing angle is about 73.7398° and the supplementary angle is 106.2602°.
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Frequently asked questions
Is the crossing angle the angle with a side?
No. The acute crossing angle is twice the diagonal angle with the longer side.
Can the diagonal equal a side?
That would make the other side zero. This tool requires a rectangle with positive area.
Are both diagonals equal?
Yes. Both use the same two perpendicular side lengths.