Calculator and formulas for calculating the parameters of a golden rectangle
A golden rectangle is a rectangle whose ratio of the two sides a and b is the golden ratio. The golden ratio is defined by (a + b): a = a: b, it is approximately 1.62.
The online calculator calculates the side lengths a and b, the diagonal, the circumference and the area for a golden rectangle. One of the values must be known. The other parameters are calculated.
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\(\displaystyle φ=\frac{1+\sqrt{5}}{2}\)
\(\displaystyle ≈ 1.618\)
\(\displaystyle b=\frac{a}{φ}\)
\(\displaystyle a=b · φ\)
\(\displaystyle d=\sqrt{a^2 · (1+1/φ^2)}\)
\(\displaystyle a=\sqrt{\frac{d^2}{1+1/φ^2}}\)
\(\displaystyle P=2·a·(1+1/φ)\)
\(\displaystyle a=\frac{P}{2 ·(1+1/ φ)}\)
\(\displaystyle A=\frac{a^2}{φ}\)
\(\displaystyle a=\sqrt{A · φ}\)
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