My Favorite Formula --CORRECTED!

I initially posted this blog Wednesday night but I made an error in the short-cut formula. Thank you to everyone who pointed out my error! (This is why I love tech editors.)

A few weeks ago, I taught a short workshop on the mathematics of knitting for the Front Range Knitting Guild. Before I go on, I’d like to thank the members for being so exceptionally nice to me as I faltered at the white board. (I'd also like to ask your patience with my bad images--I'm just learning to use a digital camera.)

At the end of the meeting, I was asked how to adapt a pattern written for one gauge to another gauge. For example, let’s say that a pattern calls for worsted-weight yarn at a gague of 5 stitches to the inch and you want to adapt it for sportweight yarn at a gauge of 6.5 stitches to the inch. Let's say that the pattern calls for casting on 98 stitches. How many stitches would you cast on to produce a piece the same width at your tighter gauge of 6.5 stitches to the inch?

1. The answer lies in a simple relationship of ratios:

2. If we plug in the numbers, we have:

3. To solve for the unknown (Number of sts at your gauge), simply cross multiply between the two ratios:

4. Then divide both sides by the Your gauge (in this case, 5):

5. Solve for the unknown number of stitches:

Because you can’t cast on partial stitches, you’d need to round up to 128 stitches (if you wanted to work with an even number of stitches) or round down to 127 stitches (if you wanted to work with an odd number of stitches).

For a short cut, simply plug in the following equation every time the pattern lists a number of stitches to determine the number of stitches to work at your gauge:

For example, if the pattern said to bind off 30 stitches at the center neck, you’d bind off 39 stitches instead.

                                     

If you chose to work with an even number of stitches initially (128 stitches), you’d want to adjust this number to be an even number as well so that there would be the same number of stitches on each side of the neck. Keep in mind that it’s your choice whether to adjust up to 40 stitches or down to 38 stitches--the difference of a stitch won't make a visible difference.

Now, I don't need to tell you to power of this little formula. It's what I used to figure out all of the additional gauges for the patterns in The Knitter's Handy Book of Patterns and The Knitter's Handy Book of Sweater Patterns.

For each project, I figured out the pattern for a gauge of 6 stitches/inch, then used this formula to determine the stitch count for all the other gauges. If there is no specific pattern repeat row-wise, you can simply knit to the specified length to the underarm, shoulder, etc. But be aware that it doesn't work as well if you're altering the gauge in a set-in sleeve cap or if your working with a stitch or color pattern that's designed to end at a particular point at the armholes, neckline, or shoulders. In these cases, the original row gauge is an important factor in the design. (But these adjustments can made as well, using the same formula along with a little practical sense.)