Is the golden ratio really used in classical art?

Far less than commonly claimed. Many attributions to the Parthenon and to Renaissance painting fail when the actual measurements are checked.

Math & Statisticsgeometry

Golden Ratio Calculator

Golden ratio divisions from any one known dimension. Phi is the only number whose reciprocal is itself minus one, which is what makes the proportion self-similar.

Also called: phi calculator, divine proportion.

Longer part

618.03

Longer 618.03, shorter 381.97, whole 1,000. The ratio is 1.62, which has the property that the whole is to the longer as the longer is to the shorter.

Shorter part

381.97

Whole

1,000

Phi

1.62

One over phi

0.62

How this is calculated

Method and background

How this is calculated

Phi satisfies the equation where the whole over the longer part equals the longer over the shorter. Solving gives (1 + root 5) / 2. The unusual property is that one over phi is phi minus one, exactly 0.618, so a golden rectangle with a square removed leaves another golden rectangle, and that recursion is why the proportion appears in design.

the only ratio where the whole is to the larger part as the larger is to the smaller

phi: The golden ratio

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a thousand unit whole

Known dimension: 1,000
That dimension is the: Whole

Longer part618.03

1000 / 1.618034

Open this example

from the longer part

Known dimension: 618.03
That dimension is the: Longer part

Longer part618.03

boundary: the inverse of the first case

Open this example

Method and limits

What it assumes

Exact phi rather than an approximation like 8:5.

What it deliberately does not model

Its aesthetic significance is much disputed, and many claimed historical uses do not survive measurement.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Is the golden ratio really used in classical art?: Far less than commonly claimed. Many attributions to the Parthenon and to Renaissance painting fail when the actual measurements are checked.