The golden ratio in logo design: what is true, and how to use it.

The famous logos, checked

The Apple logo: the circles-and-ratio diagram that circulates was drawn by a designer years after Rob Janoff made the mark in 1977, and Janoff has said plainly that he did not use the golden ratio. The circles fit because a designer chose circles that fit; you can do the same to almost any rounded shape. The Twitter bird of 2012 really was built from overlapping circles — the design team published the construction — but the circles are related by simple whole-number ratios, and the golden-ratio version of that diagram is, again, a later overlay.

Pepsi’s 2008 redesign came with a leaked agency document that invoked the golden ratio, the Mona Lisa, the earth’s magnetic field and a great deal else; it is best read as a sales pitch. The National Geographic border, on the other hand, is a genuine golden rectangle — 1.61 to 1 — and has been since the yellow frame was introduced. Toyota’s three ellipses have been fitted to golden rectangles in diagrams, with the same caveat as Apple. The honest scorecard: one clear case, one whole-number construction misdescribed, and several drawings made after the fact.

Why the myth is so sticky

A golden rectangle looks good, and a pair of compasses can make almost anything look as though it was planned. Overlaying arcs on a finished logo is satisfying in the way that finding faces in clouds is satisfying, and it produces an impressive image for a portfolio. None of that is dishonest so much as circular: the ratio is being used to explain a shape that was chosen by eye, and the eye, after two thousand years of the same buildings and paintings, tends toward proportions near it anyway.

The useful lesson is the reverse of the myth. The ratio is not a secret hidden in good logos; it is a tool you can reach for before drawing, to make a set of sizes that agree with each other. That is where it earns its place in design, and it has nothing to do with spirals.

Type scales: where it really works

Choose a body size, say 16 pixels, and multiply by 1.618 for the next size up: 26. Multiply again: 42. Again: 68. Divide for the sizes below: 10. That is a modular scale, and a golden one is the classic choice because each step is large enough to read as a different level and small enough that the levels still belong together. Most of the type on this site follows it: body text around 17, subheads at 27, headings between 42 and 68 depending on the screen. The reader never sees the arithmetic; they see a page that does not argue with itself.

The same scale works for spacing. If the paragraph gap is one unit, the gap before a heading is 1.618 units and the gap between sections is 2.618. Designers who do this by eye arrive at something close; doing it by number makes it consistent across a whole site, which is what the eye actually notices.

Layout: the golden rectangle and the section

A page or a poster laid out as a golden rectangle, with the main element at the golden section rather than the centre, is the oldest use of the ratio in design and still the most reliable. In practice: put the thing that matters 38 percent in from one edge and 38 percent down from the top, give it the larger area to sit in, and let the secondary elements take the remaining 38 percent strip. A two-column layout with columns of 62 and 38 percent feels balanced without being symmetrical; 50 and 50 feels static, 70 and 30 feels lopsided.

For a logo itself, the ratio is most useful in the relation between the mark and the wordmark — mark height to text height at 1.618 — and in the clear space around it, set at the golden section of the mark’s height. Neither will make a bad mark good. Both will stop a good mark from looking as though its parts were made on different days.

How I use it in the works

The Blueprint Fibonacci collection and pieces such as The Celestial Blueprint are drawn the way a designer would build a system: a base unit, a scale, and every element sized from the scale, with the construction left showing. The Klimt-derived works do it quietly — the mosaic bands step up by the ratio, the figure sits at the section — and the deco pieces make it the subject. The point in every case is the same as in a well-built page: nothing in the picture is a size that the rest of the picture did not agree to.