Golden Section Divider Calculator
Split a length into the golden ratio — get the longer and shorter segments so the whole is to the longer as the longer is to the shorter.
How it works
φ = (1 + √5) ÷ 2 ≈ 1.618034 · Longer = total ÷ φ · Shorter = total − longer · whole : longer = longer : shorter = φ
The golden section divides a length so that the whole is to the longer part as the longer part is to the shorter — a self-similar proportion whose ratio is φ = (1+√5)/2 ≈ 1.618. Dividing the total by φ gives the longer segment; the remainder is the shorter. Designers use this split to place a fold, a horizon line or a focal point in a way that feels balanced.
Worked example
A 100-unit line splits into a longer part of 100 ÷ 1.618 ≈ 61.80 and a shorter part of 38.20. Checking the proportion, 61.80 ÷ 38.20 ≈ 1.618 — the same φ that relates the whole to the longer part.
Sources: Golden ratio — Wikipedia
Frequently asked questions
What is the golden ratio φ?
φ is the number (1 + √5)/2 ≈ 1.618034, the unique proportion where the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. It appears in pentagons, Fibonacci ratios and countless design grids.
How is this different from a plain golden ratio calculator?
This one starts from a total length and returns the two segments that divide it at the golden section, which is what you need for layout and cropping. A general golden-ratio tool typically scales a single value up or down by φ.
Which segment is the longer one?
The longer segment is the total divided by φ (about 61.8% of the whole), and the shorter is the remaining 38.2%. Together they always add back to the full length.
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This calculator is for educational purposes. Double-check important results before acting on them.