Golden Ratio Calculator
Enter a short side, long side or total and get the golden-ratio partner lengths, the golden rectangle, the section split in % and a φⁿ ladder of sizes.
The lengths that sit in golden proportion to the one you have — for a rectangle, a layout split or a spacing ladder — with φ to ten decimals.
Example: A long side of 100 pairs with a short side of 61.803 for a golden rectangle 100 × 61.803; a 1000 px column splits 618.03 / 381.97, and the φⁿ ladder runs 38.2, 61.8, 100, 161.8, 261.8.
One number,
and where it comes from.
What φ is, how the three lengths relate, and what the ladder and the sections are for.
The ratio
A length is cut in the golden section when the whole is to the longer part as the longer part is to the shorter — Euclid's “extreme and mean ratio”. Solving that proportion gives φ = (1 + √5) / 2 ≈ 1.6180339887, the only positive number with φ² = φ + 1. So long = short × φ, total = long × φ, and the long part is always 61.8 % of the whole. Give any one of the three lengths and the other two follow; the calculator shows the rectangle, the split and both shares.
Ladder and sections
The ladder multiplies your value by φⁿ for n from −k to +k, the same way a type scale multiplies a base size by a ratio — useful for a spacing or sizing system where every step is a golden step of the last. The sections list divides the total repeatedly by φ: total / φ, total / φ², and so on, which is the sequence of nested golden rectangles (and of the classic spiral construction). Values are unit-free; use whatever unit you typed.
What it does not claim
Whether a golden proportion looks better than 3 : 2 or 16 : 9 is a design judgement, not a calculation; this page only does the arithmetic exactly. Rounding is left to you — a 61.803 px column is a 62 px column in practice. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Euclid, Elements, Book VI, Definition 3 — division in extreme and mean ratio (the golden section)
- NIST Digital Library of Mathematical Functions — φ = (1 + √5) / 2 = 1.61803 39887…
Last reviewed 19 September 2026. How results are checked: How we verify.