The
mathematics

Everything here is a number the trade already uses. Where it is a published standard I say so. Where it is a rule of thumb I say that too, because the difference matters and almost nobody marks it.

The golden ratio is real in exactly one place

It gets invoked constantly in fashion, nearly always as decoration on an argument that did not need it. There is one spot where it genuinely holds up, and it is worth knowing which, if only so you can be sceptical about the rest.

landmarkfraction of heightnearest φ valueapart by
natural waist0.6201/φ = 0.6180.3%
mid thigh0.3901/φ² = 0.3822.1%
knee0.270——
shoulder0.818——

On a body of 160 cm the golden point sits 98.9 cm from the floor. The natural waist sits at 99.5 cm. Six millimetres apart.

That is why a high waistband reads as proportioned and why the myth has such a long life. It is also the full extent of the claim. The waist is in the right place; your shoulders, your knees and your hemline are not governed by anything mystical.

The rule the trade actually teaches is thirds

Stylists divide a look one third to two thirds rather than down the middle, because an even split shortens the figure.

divisionat 160 cmwhat sits there
a third from the floor53.3 cmupper calf, which is a midi hem
two thirds106.7 cmjust above the natural waist
golden, 1/φ98.9 cmthe natural waist itself
golden, 1/φ²61.1 cmmid thigh, which is a short hem

Both survive because they land within a few centimetres of each other on most bodies, so whichever you invoke afterwards will appear to explain why something looked right. Thirds is the useful one, because you can do it in your head in a changing room.

Grading: the arithmetic between sizes

European sizes step by four centimetres in bust, waist and hip. That part is a standard and it is reliable.

sizebustwaisthipstep
EU 34826488—
EU 36866892+4
EU 38907296+4
EU 409476100+4
EU 429880104+4
EU 4410284108+4

Length is not part of that standard, and this is the whole reason this website exists. A range graded 34 to 44 covers twenty centimetres of body circumference and, very often, zero centimetres of length. Everyone in the range gets the same hem.

Which is less stupid than it sounds. A size 44 woman is not taller than a size 34 woman, so grading length with size would hand the longest skirt to the widest customer, who might be 158 cm. There is a longer version of this argument on the Why it is not done page, and it is more sympathetic than you would expect.

Ease: the gap between your body and the cloth

The most misunderstood number in online shopping. A chart of body measurements and a chart of garment measurements can differ by fifteen centimetres and both be perfectly honest.

cutease at the bustease at the hipwhat it does
negative−2 to 0 cm−4 to 0 cmonly possible with stretch
fitted1 to 4 cm0 to 3 cmskims the body, almost no spare
close5 to 7 cm4 to 6 cmfollows the body, restricts a little
standard8 to 11 cm7 to 9 cmthe default for a woven
relaxed12 to 17 cm10 to 16 cmhangs away from the body
oversized18 cm and up17 cm and upthe volume is the design

These are trade rules of thumb, not a standard. They shift by house and by category. They are the same bands the Fitting page uses when it recommends you a size, so if you disagree with a recommendation, this table is where the disagreement lives.

Stretch: what it fixes and what it does not

Elastane does not make a garment run large. It lets a smaller flat measurement fit a larger body, because the cloth supplies movement that ease would otherwise have to provide. Those are different things and the difference is the reason I am a 38 in a woven and a 36 in a knit without having changed shape.

elastaneusable give in wearcan you size downwhat it will not fix
0 to 1%almost noneno, size for your widest measurementanything
2 to 3%3 to 5 cm at the hipif you are between sizes, yeslength, shoulders, rise
4 to 6%6 to 10 cmusually, and you should if you want it fittedlength, shoulders, rise
7% and up10 cm and moreyes, and it will relax further with wearlength, shoulders, rise

Look at the last column. Stretch is a circumference solution and nothing else. You can take a 36 in a stretch trouser and still receive a 36 inseam and a 36 rise on a body that needs a 38 in both, and no amount of elastane will lengthen a leg.

The figures in that table are trade rules of thumb, not measurements. The same percentage of elastane behaves differently in different yarns: in laboratory tests on denim, recovery after stretching ran from about 57 per cent for plain cotton to about 90 per cent for cotton spun round elastane and polyester.

The bias, and why it is exactly forty-five degrees

A woven cloth barely extends along either set of threads. Cut it at 45° to both and it extends five to ten times as much and falls in a spiral.

This is geometry rather than chemistry. Forty-five degrees is the only angle at which both thread systems are equally oblique, so the cloth can deform as a lattice instead of pulling on either set of threads directly. Madeleine Vionnet built an entire house on it in the 1920s and it still looks like a trick.

direction of cutextension in a plain weavebehaviour
warp, along the grain2 to 5%holds its length, hangs straight
weft, across the grain3 to 6%a little softer
bias, at 45°15 to 30%clings, elongates, drapes in a spiral

Drape, which somebody did think to measure

The Cusick test drapes a circle of cloth over a smaller disc and measures the shadow it casts. The drape coefficient is the ratio of that shadow to the flat circle. Lower means more fluid.

clothdrape coefficientreads as
silk chiffon, fine viscose20 to 35%fluid, follows the body
crepe, soft twill35 to 55%falls close, some volume
cotton poplin, gabardine55 to 75%holds its own shape
denim, canvas, heavy linen75 to 95%stands away from the body

It is a real laboratory number with a real test method behind it, and it would answer the question every product photograph fails to answer, which is whether a dress will follow your shape or replace it.

Three things that are not mathematics

Body-type geometry. Pear, hourglass, apple. Useful shorthand for the relationship between three measurements and nothing more. There is no equation underneath, and nothing on this site uses one.

Universal proportion systems. Le Corbusier’s Modulor turns up in fashion writing with some regularity. It is architecture, and it was built on a 183 cm man.

The eight-head figure. A real adult is about seven and a half heads tall. Fashion illustration stretches the figure to eight or nine because it flatters the line of a garment, and it has been doing so for long enough that a drawing convention is now widely mistaken for anatomy. It is also, if you think about it, the same problem as the 178 cm model, a century older.

Where the body landmarks come from

The fractions in the first table — the waist at 0.620 of height, the knee at 0.270, the shoulder at 0.818 — are the foundation of every reading this site produces, so they deserve a note of their own.

Body landmarks are defined in ISO 7250 and ISO 8559, and European size labelling in EN 13402. The proportional figures used here come from national anthropometric survey data; the large European sources are SizeUK, SizeGERMANY and CAESAR.

These are population averages, and your own proportions will differ from them, which is exactly why the site asks for your inseam separately instead of estimating it from your height. The landmarks above the crotch scale with your torso and the ones below scale with your leg, and getting those two apart from each other is most of what the engine does.

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