🐚Golden Ratio Calculator

About this tool

Enter a value and say whether it's the whole length, the longer part or the shorter part. The calculator gives the other two in the golden ratio, draws a golden rectangle with its spiral arc, and lists a scale of values multiplied and divided by φ. You can use the scale for font sizes, spacing or layout widths.

What the golden ratio is and how to use it

The golden ratio, φ (phi), is (1 + √5) ÷ 2 ≈ 1.6180339887. A line is cut in the golden ratio when the whole is to the longer part as the longer part is to the shorter part. Split 100 that way and you get 61.80 and 38.20. If the short side of a rectangle is 10 cm, the golden long side is 16.18 cm. φ has some neat properties: φ² = φ + 1, 1/φ = φ − 1, and ratios of consecutive Fibonacci numbers (8/5, 13/8, 21/13…) get closer and closer to it. Cut a square off a golden rectangle and the piece left over is another golden rectangle. Joining quarter-circle arcs through those squares draws the golden spiral. Designers use φ as one pleasing proportion. A 960-pixel layout splits into a 593 px content column and a 367 px sidebar, and a 16 px body text pairs with a 26 px heading in a golden type scale. Honest limits: the golden ratio is popular, but it isn't magic. Claims that the Parthenon, the Mona Lisa, the pyramids or attractive faces follow φ precisely are mostly myths or loose fits. The rule of thirds, 3:2 or 4:3 often work just as well, so use φ as a starting point and trust your eye. The ratio calculator, the aspect ratio calculator and the type scale generator are related, and Ratios explained: how to simplify, scale, and divide an amount in a given ratio covers ratios in general.

Frequently asked questions