The mathematics
of a garment

Everything here is a number the trade already uses. Where a figure is a standard it is named as one, and where it is a rule of thumb that is said too.

I

The golden section is in the body

It is invoked constantly in fashion and almost always in the wrong place. Here is where it is genuinely true.

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 falls at 98.9 cm from the floor. The natural waist sits at 99.5 cm. They are 0.6 cm apart. That is why a high waist reads as proportioned, and why the myth persists.

II

But the rule the trade teaches is thirds

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

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

Why both survive. They land within a few centimetres of each other on most bodies, so either can be invoked afterwards to explain why something looked right. Thirds is the useful one, because you can find it in your head.

III

Grading — the arithmetic between sizes

European sizes step by four centimetres in bust, waist and hip. That part is a standard. Length is not.

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

The consequence. A range graded 34 to 44 spans twenty centimetres of body circumference and frequently zero centimetres of length. Every customer in that range receives the same hem.

IV

Ease — the gap between the body and the cloth

The most misunderstood number in online sizing. A chart listing body measurements and one listing garment measurements can differ by fifteen centimetres and both be correct.

cutease at the bustease at the hipwhat it does
negative−2 to 0 cm−4 to 0 cmonly possible with stretch
close0 to 4 cm0 to 4 cmfollows the body, restricts a little
standard5 to 8 cm4 to 8 cmthe default for a woven
relaxed9 to 15 cm8 to 14 cmhangs away from the body
oversized16 cm and up15 cm and upthe volume is the design

Trade rules of thumb rather than a standard. They vary by house and by category.

V

Stretch — what it solves 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 the movement that ease would otherwise provide. That is a different thing.

elastaneusable give in wearcan you size downwhat it will not fix
0 to 1%almost noneno — size for the 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 — it will relax with wearlength, shoulders, rise

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.

VI

The bias — forty-five degrees

A woven cloth barely extends along either thread. Cut at 45° to both it extends by five to ten times as much and falls in a spiral. This is geometry, not chemistry: it is the angle at which both thread systems are equally oblique.

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
VII

Drape, measured

The Cusick test drapes a circle of cloth over a disc and measures the shadow it casts. The coefficient is the ratio of that shadow to the flat circle. Lower means more fluid. A real laboratory number that almost no brand publishes.

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
VIII

What is not mathematics

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

Universal proportion systems. Le Corbusier’s Modulor is architecture, not tailoring, and it was built on a 183 cm man.

The eight-head figure. A drawing convention. A real adult is about seven and a half heads tall; fashion illustration stretches to eight or nine to flatter the line. A rendering choice mistaken for anatomy for a century.

TOILE
where it falls · Method I