Golden ratio face calculator: how close is your face to 1.618?

How the golden ratio face calculator works

A face model running in your browser places 478 points on your face. We level the photo on the line down the middle of your face, find your hairline, and measure the five pairs that golden ratio face analysis compares with 1.618:

• Face length to width: hairline to chin, divided by the widest span of your face.
• Mouth to nose width: corner to corner of your mouth, divided by the width of your nose wings.
• Nose length to width: the top of your nose bridge to the base of your nose, divided by its width.
• Lips to chin: from where your lips meet to your chin, divided by the space from your nose to your lips.
• Lower to upper lip: the height of your lower lip, divided by the height of your upper lip.

Each match is 100% minus how far your ratio is from 1.618, as a share of 1.618. A ratio of 1.50 is 7% short of the golden ratio, so it matches 93%. Your golden ratio match is the average of the five. The table also checks the facial thirds and fifths against their own ideal of 1, and draws every line on your photo: gold for what is measured, white for what it is divided by.

Your hairline is estimated. The face model stops on the upper forehead, so we look for the line where the color of your forehead turns to hair, and estimate it from the shape of your forehead when hair covers it or the photo cuts it off.

How to read your golden ratio results

Each row of the table gives your ratio, the ideal, and your match. The little ruler beside the match shows the direction: the tick in the middle is the ideal, and your dot sits to the left when your ratio is under it and to the right when it is over. Point at a row, or tap it on a phone, and its lines light up on your photo while the rest fade back.

The chips above the table switch the layers on your photo: the phi grid, the five golden pairs, the thirds, and the fifths. The strips under the table show the same thirds and fifths as shares, so you can see at a glance which part of your face runs long or short.

If your face length ratio sits under 1.618, that is no surprise. A golden face is long and narrow: a face 14 cm wide would have to run about 22.7 cm from hairline to chin to hit it. A lower number there simply means your face is wider for its length than the golden template.

What is the golden ratio?

The golden ratio, written φ (phi), is about 1.618. You get it when you split a line so that the whole is to the longer part as the longer part is to the shorter. Euclid described it in the Elements as dividing a line in “extreme and mean ratio.” Luca Pacioli called it the divine proportion in a book published in 1509, and the name “golden section” first appears in print in 1835 (MacTutor History of Mathematics).

A golden rectangle, 1 wide and 1.618 tall, has a neat property: cut a square off it and what is left is a smaller golden rectangle, again and again. Join those squares with quarter circles and you get the golden spiral. That is the phi grid on your photo, sized to the width of your face, so you can see at a glance where a face of golden proportions would end.

Is the golden ratio face real?

The math is ancient. The idea that beautiful faces follow it is far younger, and its best-known form is the “phi mask” of maxillofacial surgeon Stephen Marquardt, a face template built from golden ratio proportions that some surgeons and orthodontists have used as a target. Researchers have pushed back hard. A review in Aesthetic Plastic Surgery found the mask best describes the masculinized faces of white fashion models, fits many other populations poorly, and warned against using it as a goal for surgery (Holland, 2008).

Experiments point somewhere else. When Pallett, Link, and Lee moved the eyes and mouth around on the same faces, the versions rated most attractive had an eye-to-mouth distance of about 36% of face length and a gap between the eyes of about 46% of face width, the proportions of an average face rather than golden ones (Vision Research, 2010).

There is a statistical catch too. A face has dozens of distances you could measure, so a few pairs will land near 1.6 on almost anyone. That is why this calculator uses a fixed list of pairs, chosen before it sees your photo, and shows you every one of them, close or not.

Facial thirds and fifths

Long before the phi mask, artists drew faces with simpler canons: three equal heights (hairline to brows, brows to the base of the nose, nose to chin) and five equal widths, each one eye wide. When Leslie Farkas and colleagues measured young North American adults, many faces did not follow these canons (Farkas et al., 1985), and they have held up no better in other groups since. The strips under your result show how your own face divides, against the canon’s equal shares.

How to take a photo for the golden ratio test

Ratios are only as good as the photo. The biggest error is the camera’s distance: a phone held close works like a wide-angle lens, makes your nose look wider, and lowers your mouth to nose ratio.

1. Shoot from at least arm’s length, or prop the phone up and step back with the 2x lens.
2. Hold the camera at eye level, chin level, and look straight into the lens.
3. Keep a neutral face with your lips closed. A smile stretches your mouth and lowers your chin.
4. Pull your hair back from your forehead and from the sides of your face, which set your width.
5. Use soft, even light from the front, so shadows don’t hide the edge of your jaw.

Want a single number instead of a lab report? The attractiveness test turns these proportions, your symmetry, eye tilt, and jawline into a face score out of 10. For balance, try the face symmetry test; for your outline, the face shape detector and the guide to the six face shapes.