Golden Ratio Calculator

What this tool does

Two parts are in the golden ratio when the whole is to the larger part as the larger is to the smaller: φ ≈ 1.618. A line of 100 splits into about 61.8 and 38.2. Designers use it for proportions of pages, frames and logos, and photographers' 'phi grid' places lines at 38.2 % and 61.8 % instead of the thirds. Claims that it rules beauty or appears everywhere in nature are mostly overstated — it is one pleasant proportion among several.

Formula

φ = (1 + √5) ÷ 2 ≈ 1.618 · larger = L ÷ φ · smaller = L ÷ φ²

Variables

Worked example

Limitations

• The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.