Golden Ratio Face Calculator

The golden ratio is a number, written with the Greek letter phi, that appears when a line is split so that the whole relates to the longer part as the longer part relates to the shorter one. It has a long history in mathematics and art, and over time people have claimed to find it in buildings, shells and faces. Some of those claims hold up loosely; many were found by choosing which points to measure after the fact.

For faces, the idea became popular through proportion guides and masks sold in cosmetic and dental practice, which overlay a grid of golden-ratio lines on a face. These are design conventions. They can be a useful vocabulary for describing proportions, but they are not a measured definition of beauty, and faces that people find attractive vary widely across cultures, ages and individuals.

All four ratios come from the landmark points on your photo, measured after the face is levelled using the eye line. The rule of fifths (eye width against the gap between the eyes) is not included: the model's eye-corner points are too rough for it and would give nearly everyone the same wide-set reading.

• Mouth width to nose width: the span between the mouth corners against the outer nostril points, shown next to 1.618. The nostril points sit a little inside the widest part of the nose, so this ratio tends to read higher than a ruler would.
• Face width to brow-to-chin length: a golden face is 1.618 times as long as it is wide, and with equal thirds the brow-to-chin part is two thirds of that length, so the reference here is about 0.93.
• Facial thirds: the middle third (brow to the base of the nose) against the lower third (base of the nose to the chin); the classical guide has them roughly equal.
• Lower-third split: lips to chin against nose base to lips; drawing guides often use one part above the lips to two below.

Classical guides split the face into three equal parts: hairline to brow, brow to nose base, nose base to chin. The 68-point landmark model places points on the brows, eyes, nose, mouth and jaw, but none on the hairline, so there is no reliable point to measure the top third from. Rather than guess, the tool measures only the middle and lower thirds and leaves the upper third out. For the same reason, any length that would need the hairline is taken from the points the model does have, so it will not match a tape-measure reading of your face.

Each ratio is shown as your value next to the reference, so you can see whether it sits above or below and by how much. Being close to a reference is not better, and being far from it is not worse: the references describe one tradition's idea of balance, and real faces sit all around them. The useful reading is comparative. Do two photos of you give similar values? Does a different angle change the face length ratio? Which ratio moves most when you smile?

The ratios are also sensitive to small landmark errors. A point placed a few pixels off on a small face can shift a ratio noticeably, which is another reason to use a sharp, well-lit photo where the face fills a good part of the frame.

Studies that test golden-ratio proportions against people's ratings of faces have found weak and inconsistent links. Average proportions differ between populations, between men and women and across ages, so a single ideal number cannot fit everyone. The ratios here describe one photo, taken with one lens from one angle, and change with head turn, camera distance and expression. Read them as a measurement, never as a verdict on anyone's appearance.

• Stand back and zoom slightly rather than holding the phone close; close lenses widen the nose and narrow the face.
• Keep your head level and facing the lens; turning shortens one side of the face.
• Keep a neutral mouth; a smile widens the mouth and changes the nose-to-mouth ratio.
• Move hair off the brows and jaw so the landmarks find the real outline.
• Check the left-right balance on the face symmetry test page with the same photo.