Golden Ratio Calculator
Enter a total length and split it into a longer and a shorter part in the golden ratio φ ≈ 1.618 — the proportion artists, designers, and nature itself keep coming back to.
What is the golden ratio?
The proportion phi ≈ 1.618
This golden ratio calculator splits a total length into two parts so that the longer part divided by the shorter part equals φ (phi) ≈ 1.618. Phi is defined as φ = (1 + √5) / 2, and it has a self-similar property no other number shares: the whole relates to the longer part exactly as the longer part relates to the shorter part. That single proportion turns up again and again — in the spiral of a nautilus shell, the seed pattern of a sunflower, the framing of paintings and photographs, and the layout of pages and logos. It is closely linked to the Fibonacci sequence, whose consecutive terms (1, 1, 2, 3, 5, 8, 13…) settle ever closer to φ.
Enter a total length and instantly get the longer part (total ÷ φ) and the shorter part in the golden ratio.
To divide a length in the golden ratio, divide the total by φ to get the longer part, then subtract that from the total to get the shorter part. The two parts then sit exactly in the proportion φ.
longer = total ÷ φ, shorter = total − longerTake a total length of 100. Dividing by φ gives a longer part of 61.803399, and subtracting that from 100 leaves a shorter part of 38.196601. Check the proportion: 61.803399 ÷ 38.196601 = 1.618 = φ, exactly as the golden ratio requires. Because φ is a fixed number, the split scales with your input — a total of 200 simply doubles both parts to 123.606798 and 76.393202, keeping the same ratio.
The arithmetic is exact, but a couple of points are worth keeping in mind when you apply the result.
A proportion, not a rule, and an irrational number
φ is irrational, so the parts are rounded here to six decimal places — fine for design and layout, but round to your own tolerance for physical cuts. The golden ratio is also an aesthetic guideline, not a law: many famous claims about it in art and architecture are debated, so treat it as a balanced starting point rather than a guarantee of beauty.