This is something I rediscovered that is

very obvious and everyone including myself already knows it, but I managed to forget it in the swamp of "learning to draw". Hopefully it is sort of helpful, or hopefully you already know this and keep it in mind when drawing. Its half a rant at myself for forgetting as well.

**Two point summary at the bottom for those who think I talk too much**So, all of us have heard of proportions when drawing. I think almost all of us have recommended it to everyone else at some point, "You should work a bit on proportions", or "I need to do more studies on proportions".

But somehow, possibly through overuse of the word, I managed to forget what it actually means. It sort of ended up meaning "looks real" or "looks right", which is still a correct understanding of the word, but not how it applies when I actually draw.

Its a lot easier to tell something is wrong, than to be able to draw it right from the beginning.Looking up "Proportion","Proportionality" etc on Wikipedia, You get these results: (I've highlighted the bits I think are important)

Proportionality (mathematics)

In mathematics, two variables are proportional if there is always a constant ratio between them. (Variable y is directly proportional to the variable x.)

Proportion (architecture)

Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole. These relationships are often governed by multiples of a standard unit of length known as a "module".(In classical architecture, proportions were set by the radii of columns.)

Body proportions

While there is significant variation in anatomical proportions between people, there are many references to body proportions that are intended to be canonical, either in art, measurement, or medicine.

In measurement, body proportions are often used to relate two or more measurements based on the body. A cubit, for instance, is supposed to be six palms. A span is taken to be 9 inches and was previously considered as half a cubit.

It is important in figure drawing to draw the human figure in proportion (duh). Though there are subtle differences between individuals, human proportions fit within a fairly standard range, though artists have historically tried to create idealised standards, which have varied considerably over different periods and regions. In modern figure drawing, the basic unit of measurement is the 'head', which is the distance from the top of the head to the chin. This unit of measurement is reasonably standard, and has long been used by artists to establish the proportions of the human figure. Ancient Egyptian art used a canon of proportion based on the "fist", measured across the knuckles, with 18 fists from the ground to the hairline on the forehead.

The ancient Greek sculptor Polykleitos [...] wrote an influential Canon describing the proportions to be followed in sculpture [which] applies the basic mathematical concepts of Greek geometry, such as the ratio [and] proportion,[...] creating a system capable of describing the human form through a series of continuous geometric progressions. Polykleitos uses the distal phalanx of the little finger as the basic module for determining the proportions of the human body, scaling this length up repeatedly by root 2 to obtain the ideal size of the other phalanges, the hand, forearm, and upper arm in turn.

Aspect Ratio

The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side – the ratio of width to height,(when the rectangle is oriented as a "landscape")

The aspect ratio is most often expressed as two numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the relationship between width and height. As an example, 8:5, 16:10, 1.6:1, ?8?5 and 1.6 are all ways of representing the same aspect ratio.

So what did all that text actually mean?

Simply restating it, proportion is

how sizes relate to one another, or how one size/length/dimension compares to another. Its the ratio of lengths, such as 1:2 forearm:whole arm.

Typically as stated above, artists use a base measurement that is a constant in their drawing, such as head height, and then use multiples which govern the overall character height, the torso height and the leg height, to name a few. This ratios have an

actual number attached, such as "7 heads high character".

**So "proportions" means, a list of lengths of objects (typically body parts) as multiples or fractions of a standard unit (typically head)**As beginner artists, we often draw these divisions to count out the multiples.

But at some point, we stop doing this, and go by eye a lot of the time, or at least, I do. This is because we start to get a general feel for the 1:7 ratio (for example) without having to count it out. But I think this leads to stylisation occurring sooner or later, as our drawings start to skew towards easier ratios, and we tend to approximate a lot more, rather than measuring out.

I'm not suggesting that we keep drawing little rulers all over the place with divisions to keep a track of exact ratios, but bear in mind that for the same character or person, their proportions NEVER change (minus age progression etc) They are the same person so they will always have "a slightly longer chin", or "longer arms than average".

**WAIT!!!** What does "slightly" or "average" mean? these words can change depending on our mood, what we last drew, be it figure drawing or "cartoons", and so on. If we want to draw the same character consistently, or have a consistent art style, we need to put

actual numbers on this stuff, so we should be saying "arms are 10% longer than 2 heads" or "head is 90% of normal head size".

**Excercises**It helps to be able to split up dimensions in your head accurately. To see if you can do this, draw two marks about 6-8 inches apart on a piece of paper. Without measuring, draw a mark at 1/2 way between. Measure the distances and see if you got it right, or how far out you were. Repeat for standard measurements such as 1/3, 1/4 etc. Do the same for multiples, draw two marks about 1-2 inches apart, then draw marks at x2,x3,x4 etc distances. Lets see if we can transfer a dimension. Draw 2 marks at the top of the page, 1-4 inches apart horizontally. try and draw the same gap vertically. Draw a central (or slightly off to prevent accidental cheating with the paper edges) cross, and try and draw 8 compass points at the same distance from the center.

Heres my attempt, a minute after writing the above:

I've red-lined the correct measurements and drew in some faint lines after so you can make sense of the original marks

I hope you do better than me

So what do

~~we~~ I learn?

~~How to quantify how much I suck at drawing~~ That

even a simple proportion is difficult to measure to the eye, so trying to draw such a proportion while also juggling character design, pose, shading, form etc, will be much more difficult.

What is the solution?1) Practice. Like anything else, correctly measuring things by eye is a learned skill. When at work, I learnt to tell the thickness of the wood boards by 1/2mm intervals 2mm up to 15mm. I couldn't do it at the beginning and had to keep measuring, but got used to it. So I KNOW this is something that can be learned. The advantage is that this skill can be transferred traditional-digital, and uses a small amount of time once mastered. The disadvantage is that we already have enough to learn with art without adding more stuff.

2) Measure. Most digital art programs have guidelines and rulers that can be used, or you can copy and paste the part you want to measure to get the distance. traditionally is even easier in this aspect as a ruler is a lot more available and user friendly. The advantage is that it is 100% accurate and relatively quick to use, but digitally each program has its differences and so may be a hassle if it doesn't suit you, and traditionally you might not want to carry a ruler around with you if you want to travel light.

Also, use an appropriate base measurement. Just because most people use a head as the base length doesn't mean you have to. As stated from Wikipedia, the Ancient Egyptians used proportions based on the fist. Was it wrong? No, because it is a RATIO, so as long as you know how many units long something is, you're good to go. You could use fractions of your paper width (I have done this) or screen width if you wanted. (but watch out for zoom on the latter)

Once you are very experienced with drawing these proportions, you can

probably (don't know, haven't got there yet) go back to the "feel" of it and you would be alright, but for us that can't draw as we would wish, thats not an option for us. We wouldn't be worrying about proportions if we could already draw it correctly by "feel".

**So what are the main points?**-Keep an

exact numeric ratio of the parts of the character you are drawing in your head, or write it down.

("Bob - 7 heads tall. eyes dead center on head, eyes 1/5 heads wide with 1/5 head gaps. arms 3 heads from center of shoulder to center of wrist")

-Learn to

accurately draw these proportions by using an appropriate measurement tool or learning to judge it

correctly by eye.

(Traditional ruler, Digital guidelines/ruler, Practice drawing fractions and multiples of head lengths)

As usual, sorry for the wall of text. You can tell I'm serious when there aren't smiley faces everywhere :P

(Needless to say I copied this to a notepad before posting just in case)

(Took 2 hours to write this)

See also for

~~fun~~ reading:

https://en.wikipedia.org/wiki/Mathematics_and_artEdited for

~~adding awesomeness~~ typos