Golden Rectangle Calculation
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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Formulas for the Golden Rectangle
Ratio \(φ\)
\(\displaystyle φ=\frac{1+\sqrt{5}}{2} ≈ 1.618\)
Side length (b)
\(\displaystyle b=\frac{a}{φ}\)
Side length (a)
\(\displaystyle a=b · φ\;\;\;\;\) \(\displaystyle =\sqrt{A · φ} \;\;\;\;\) \(\displaystyle =\sqrt{\frac{d^2}{\displaystyle 1+\frac{1}{φ^2}}} \;\;\;\;\) \(\displaystyle =\frac{P}{\displaystyle 2 ·\left(1+\frac{1}{φ}\right)}\)
Diagonal (d)
\(\displaystyle d=\sqrt{a^2 · \left(1+\frac{1}{φ^2}\right)}\)
Perimeter (P)
\(\displaystyle P=2·a·\left(1+\frac{1}{φ}\right)\)
Area (A)
\(\displaystyle A=\frac{a^2}{φ}\)
Square • Rectangle • Golden Rectangle • Rectangle to Square • Rhombus, given varios parameter • Rhombus , given diagonal e, f • Parallelogram, given 2 sides and angle • Parallelogram area, given side and height • Trapezoid • Cyclic Quadrilateral • General Quadrilateral • Concave Quadrilateral • Arrowhead Quadrilateral • Crossed Square • Frame • Kite, given 2 diagonal and distance • Kite Area, given 2 diagonal • Half Square Kite • Right Kite"
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