Golden Rectangle Calculation

Calculator and formulas for calculating the parameters of a golden rectangle

Calculate golden rectangle online


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.


Calculate golden rectangle

 Input
Argument type
Known value
Decimal places
 Results
Side length a
Side length b
Diagonal
Perimeter
Area


Formulas for calculating the golden rectangle


Golden ratio\(φ\)

\(\displaystyle φ=\frac{1+\sqrt{5}}{2}\)

\(\displaystyle ≈ 1.618\)

Side length \(b\)

\(\displaystyle b=\frac{a}{φ}\)

\(\displaystyle a=b · φ\)

Diagonal \(d\)

\(\displaystyle d=\sqrt{a^2 · (1+1/φ^2)}\)

\(\displaystyle a=\sqrt{\frac{d^2}{1+1/φ^2}}\)

Perimeter \(P\)

\(\displaystyle P=2·a·(1+1/φ)\)

\(\displaystyle a=\frac{P}{2 ·(1+1/ φ)}\)

Area \(A\)

\(\displaystyle A=\frac{a^2}{φ}\)

\(\displaystyle a=\sqrt{A · φ}\)


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