Human Proportion
The Mathematics of the Human Form
The span of a man's outstretched arms is equal to his height.
— Leonardo da Vinci (after Vitruvius)
Overview
Leonardo's studies of human proportion are the foundation of the Vitruvian Man — that iconic drawing of a figure inscribed in both a circle and a square. But behind the famous image is a vast body of meticulous measurement: ratios of face to head, hand to arm, foot to leg, all reduced to precise mathematical relationships.
These measurements served a practical purpose for the painter: they allowed him to construct a convincing human figure from any angle, at any scale, without a live model present. They are the painter's equivalent of an engineer's reference tables.
Proportions of the Whole Figure
The body as a system of ratios
- From the chin to the starting of the hair is a tenth part of the figure.
- From the junction of the palm of the hand as far as the tip of the middle finger a tenth part.
- From the chin to the top of the head an eighth part.
- And from the pit of the stomach to the top of the chest is a sixth part.
- And from the fork of the ribs as far as the top of the head a fourth part.
- And from the chin to the nostrils is a third part of the face.
- And the same from the nostrils to the eyebrows, and from the eyebrows to the starting of the hair.
- And the foot is a sixth part, and the forearm to the elbow a fourth part. The breadth across the shoulders a fourth part.
C.A. 358 r. a
Proportions of the Face
The geometry of expression
The face in itself forms a square, of which the breadth is from one extremity of the eyes to the other, and the height is from the top of the nose to the bottom of the lower lip, and what is left over above and below this square has the height of a similar square.
The ear is precisely as long as the nose.
The space between the eyes is equal to the size of one eye.
In profile the ear is above the middle of the neck.
MS. A 63 r.
The foot from the toe to the heel goes twice into the space from the heel to the knee, that is to say where the bone of the leg is joined to that of the thigh.
The hand as far as where it unites with the bone of the arm goes four times into the space from the tip of the longest finger to the joint of the shoulder.
MS. B 3 v.
Every man at the third year is half his height.
MS. H 31 v.
People see the Vitruvian Man and think "art." Leonardo saw it and thought "engineering specifications." Every ratio here was measured from real bodies. This isn't aesthetic idealization — it's data. -D