Dyeing Math and Terminology

Many of the people I know who are into fibre are not math people.    Just seeing all the % signs and cryptic abbreviations like “WOF” makes them curl up in a ball.  Well, not quite, but it does make something that should be enjoyable a little bit less so.  So to combat this terrible trend, I’m going to do my best to explain, in simple terms, some of the terminology used in dyeing and how to do some of the basic calculations required to get approximately the colour you want.  I’m mainly going to focus on the ones used for Procion MX dyes for cellulose fibres and Acid dyes for plant fibres, because they are the ones I’m the most familiar with.

WOF stands for Weight Of Fibre.  This is the first thing you measure, and it’s the number you base all of your calculations on.

DOS stands for Depth Of Shade.  Essentially, how dark do you want it?  A given fibre can only absorb so many dye particles.  Sometimes if you’re going for a really dark colour you pile in more dye than it can possibly absorb, just to be sure that each available site that a dye particle can latch onto is full.  The limit is different for each dye, so until you’re comfortable with the dyeing, you probably want to do a few tests at different depths of shade to see which one you want, especially if you’re trying to match a particular colour.  The instructions that come with your dye should tell you approximately what the percentage of the weight of fibre should be to give you light, medium and dark shades.  With Procion MX, for example, .5-1% DOS is light, 2-3% DOS is medium, and 4-5% DOS is dark.  Recipes will often leave off the ‘DOS’ and simply say something like “wool is usually dyed at 1% for a full shade.”  Or they’ll say “use 4-8% cochineal bugs to WOF.”  Which makes sense . . . until you start doubting and double-thinking, and then you get confused again.  At least I do.

Stock Solution is a pre-mixed solution of dye and water.  You cannot make a stock solution of Procion MX because of the nature of the dye – it will fix to the water particles, and by the time you stick your fabric in it a week later, there are no available dye particles left.  Acid dyes, however, do very well with a stock solution.  You can make a solution any concentration you want, but for ease of calculations I usually do a 1% solution – one gram of dye per 100 mL of water.  Then if I want to dye 42 g of silk to a 1% DOS, all I have to do is measure out 42 mL of stock solution, and I’m all set.

Percentages. Time for a bit of real math now, yes?  I’ve found that everybody has their own system of figuring out percentages of things, and you probably have already practiced this without thinking about it, whether you were calculating taxes on a bag of chips or figuring out what the actual price is on those shoes that are 30% off.  Some people count back decimal places.  Some people think better in fractions.  Some people even (and this one I’ve never gotten the hang of) use the % button on their calculator.  A friend of mine can only multiply anything in his head by adding.  I’m a convert-the-percentage-to-a-decimal-and-figure-it-out-from-there girl.  Sometimes it’s really easy to do in your head, like 5% 0f 500 g.  But then what do you do if it’s 12% of 368 g of luxurious cashmere (it’s fantasy land, why not make it good?)?  I’m going to go through a couple of different sequences of number-punching on a calculator so if it’s been a long time since Math 8 (heck, it’s a long time for me, and I’m pretty much the definition of a spring chicken) then hopefully one of these methods will stick in your head well enough that you don’t have to do it six times for each calculation just to be sure you did it right.

Method 1: Decimalize! Hey, let’s do my way first.  The way I do it is to think of the numbers not as percentages, but as decimal points.  So 12% is .12, 8% is .08, and 70% is .7.  The only time this way can be confusing is with percentages that are less than 10 or more than 100.  With less than ten, you have to remember to stick a 0 in front.  More than a hundred, you’ll have a whole number and then a decimaled number (437%=4.37).  To calculate how much dye you need to do 12% DOS on 368 g, you multiply the percentage-turned-decimal by the weight.  So the actual buttons you would push are:  [.][1][2][x][3][6][8][=] and it will tell you the answer! (It’s 44.16, I’m sure you’re just burning to know what it is, assuming you haven’t calculated it yourself already).

Method 2:  Divide and Multiply!*  Another method that I use sometimes, usually if I’m confusing myself with a percentage that’s greater than 100.  This way bypasses the convert-to-decimal step of Method 1.  What you do is take you WOF (let’s use 692 this time, just for fun), divide it by 100, and then multiply the answer by whatever percent of 692 you wanted.  Say, 423%.  The calculator buttons: [6][9][2][/][1][0][0][x][4][2][3][=]  . . .  2927.16!  So if your recipe called for 423% WOF dyestuff (hmm, must be a natural dye!) and you have 692 g of fibre, then you’ll need 2927.16 g of dye.    *You have no idea how hard it was not to type “Divide and Conquer”!

You want to practise either one of these methods or your own until you can do it quickly and easily.  Almost all dye recipes require you to calculate the weights of more than one ingredient, some go as many as four or five.  If you’re doing it for fun then there’s no big time crunch looming at you, but nobody wants to do something that makes them flustered and frustrated.

Colour Mixing. The last little bit that I’m going to cover is colour mixing.  Now, there are enough colours out there that you can dye any fibre you want and get almost any colour.  But sometimes you have a particular one in mind, that’s in between the shades that are commercially available.  Or you have a shortage of storage space and you only want to keep four or five colours on hand.  Or you just like the idea that nobody else out there will ever dye something quite exactly that shade of purple.  The trouble with mixing colours (as far as the math is concerned) is that now you’re dealing with a percentage of a percentage.  For example, you have a 320 g of silk hankies that you want to dye a really lovely olive green, to a DOS of 2%.  You calculate that out, and discover that you need 6.4 g of dye.  As it happens, you don’t have a pre-mixed olive on your shelf, but you do have yellow and black.  Well, you’re in luck – you know that you can get a nice olive green by mixing yellow and black in about a 9:1 ratio, or 90% yellow and 10% black.  The total amount of dye remains the same, 6.4 g.  Now you need to do a second calculation, to find out how much 90% and 10% of 6.4 are, to discover the amount of yellow and black each you’ll need.  The answer is 5.76 g of yellow, and .64 g of black.  You can do the same thing mixing two, three, even four colours together.

One last thing:  Keep records!  Keep sample books!  Try to always throw in a bit of extra fabric/yarn/fibre and stick it in a binder with a note of the fibre, the dye, and the colour ratios you used.  It will save you from extra work doing samples every time you want to dye something, you can just look in your book and think “well, I want it pretty much like that, just a bit darker (or yellower, or paler, or more intense)” and you can look at your numbers, fudge them in the direction you want, and odds are you’ll come out pretty close to what you were looking for.  Plus, if your best friend/daughter/boss loses one of her favourite mittens that you dyed for her, then you are much more likely to be able to replicate the colour if you wrote down what you did, rather than having to guess and start from scratch.

Do I do this?  Absolutely not.  But I did in school (’cause I had to) and I often tell myself off for not doing it now.  And it’s amazing the number of times I’ve pulled out my school sample books to peruse them for ideas.

Now, if just one persone reads this and shouts “Eureka!” (I’ll settle for “oh!” or “I get it now!” but eureka would be best) then my job here is done.

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3 Responses to “Dyeing Math and Terminology”

  1. alpha Says:

    brother this is a good data u provided but i need some more information about dyeing calculations can u pl z provide me Ur mail address.

  2. alpha Says:

    sir i sended u an emails plz check

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