Face proportions: what the rules claim, and what measurements show

Leonardo did not use the golden ratio on faces

Almost every page about facial phi opens with Leonardo. It is not true, and the correction comes from inside the field. Naini's 2024 review in Maxillofacial Plastic and Reconstructive Surgery states it plainly: "Contrary to popular speculation, Leonardo da Vinci did not employ the golden ratio in any of his human-proportional drawings." He knew the ratio well enough to draw the polyhedra for Pacioli's book about it, and never once applied it to a face.

You can check the primary source yourself. The text Leonardo transcribed around Vitruvian Man is Vitruvius, Book III: the face is "a tenth part of the whole height," the head "an eighth," the foot "one sixth," and the face divides into three equal parts from chin to nostrils, nostrils to brow, brow to hairline. Tenths, eighths, sixths, thirds. Whole numbers throughout. There is no 1.618 and no irrational number anywhere in it. Naini notes the same of the drawing: "the proportions of the figure do not actually match it, and Leonardo's own text above and below the image only mentions whole number ratios."

Nor did Pacioli claim what he is credited with. His 1498 De Divina Proportione is "predominantly on mathematics and perspective in art," and he did not argue the ratio was the secret of beauty. Euclid, further back still, "merely regards it as a rather general mathematical ratio" with "no relationship to beauty or any other aspect of the natural world."

Naini also names the methodological trick that keeps phi alive, and it is the reason this page reports eight signed deviations instead of one verdict: "Admirers and supporters of the golden ratio begin with the ratio in mind, then attempt to prove its existence in the attractive human face. The choice of landmarks is often arbitrary, as is head positioning in photographs, making the genuine test and subsequent confirmation or refutation of the theory appear unverifiable." Pick your landmarks after you know your answer and phi appears everywhere. Fix them in advance, publish the gaps with their signs, and it does not.

The fWHR range everyone quotes is not in the paper they cite

Facial width-to-height ratio turns up constantly alongside golden-ratio content, usually with a population range of "1.6 to 2.15" attributed to Carre and McCormick's 2008 paper in Proceedings of the Royal Society B. We read that paper in full: methods, results, all of Table 1 and all four figure captions. The strings "1.6" and "2.15" do not appear in it, and it states no population range for fWHR anywhere. The only range in the entire text is about correlation coefficients, which "ranged from 0.17 to 0.51."

The only fWHR values the paper contains are two means from 88 undergraduates: women 1.80, men 1.86. No minimum, no maximum, no spread. The circulating range appears to have been read off the x-axis of a scatter plot and then repeated from site to site without anyone opening the paper.

It is also a different kind of measurement from anything on this page. fWHR is descriptive, from evolutionary psychology, defined as cheekbone width over the distance from brow to upper lip, and it was studied against aggression rather than beauty. It has no target value. There is no good fWHR. Phi-based ratios are the opposite: a number a face is said to should approach. Putting them side by side, as many pages do, treats a descriptive variable and a prescriptive ideal as the same kind of thing.

The authors' own caveat undercuts photo measurement generally, and applies to us as much as to anyone: the relationship they found "was partly influenced by the posture of the head in the photographs," some subjects were smiling, and they note that angry expressions lower the brow and raise the upper lip, "a pattern of muscle activity that increases the facial width-to-height ratio." Measured from a photo, that ratio is partly a measure of expression and head tilt rather than of bone.

Which facial third is longest, and why the canon almost never holds

The equal-thirds rule is the oldest item on this page, inherited from Vitruvius through the Renaissance. Measured on real people, it essentially never holds.

Which third is longest has no single answer either, and that is the more interesting result. In the Hong Kong sample the lower third was longest in 49% of men, while the middle third was shortest in 52% of women. In the Turkish sample of 200 the pattern reverses outright: the middle third was longer than the lower third in 71% of women and 65% of men. In the Saudi sample the lower third was longer in about 90% of both sexes. So "the lower third is the longest," repeated everywhere without a qualifier, is a majority tendency in some populations and simply false in others.

The Turkish authors draw the conclusion we would: these proportions "cannot be a guide for planning surgical or non-surgical treatments," and "the neoclassical canons may fit a few subjects and they do not represent the average facial proportions."

One definitional warning, because it affects the two thirds ratios above. Several of these studies measure the upper third from the hairline to the nasion, while the classical canon and most clinical teaching use the hairline to the glabella. They are not the same distance and their numbers should not be pooled.

Measure your own

Every proportion above is one a tool can read off a photo. Ours reports the eight classical ratios with a signed gap for each, so you can see which of the canons your own face declines to obey.