# Knitting Math: Calculating Cast on Stitches

Please check out the companion video to this blog post!

I was planning a rectangular shawl project called Mini Bubbles but I wanted to make it wider and knit it horizontally, rather than vertically. Fortunately, someone had already knit the same shawl using the same yarn and was kind enough to include enough information that I was able to use for my calculations.

The other knitter cast on 123 stitches and her finished measurement was 31" wide.  I wanted

These are some of the bubbles that I have opened.

my shawl to be closer to 54 inches wide. This is a shawl that will be heavily blocked so I knew there is a little wiggle room on the width.

First I needed to determine her gauge, or stitches per inch. The standby, of course, is to knit a gauge swatch. But for a shawl where measurements don't need to be exact, I am using the existing project's stitches per inch information.

Stitches per Inch Formula: Total # of Stitches/Total # Inches = # Stitches per Inch

She cast on 123 stitches and the finished project was 31" wide.  Using the formula, I calculated the following: 123 stitches/31 inches = 3.97 stitches per inch

Total Stitches Needed Formula: Stitches per Inch X Desired Inched = Total Stitches Needed

I want my shawl to be about 54 inches wide so I needed to use this next formula and figure out how many stitches are needed: 54 Inches X 3.97 Stitches per Inch = 214.38 Stitches

Knowing that I need to round the number to the nearest whole number (I won't be casting on .38 stitches) and the pattern for the shawl has a certain number of stitches, I needed to do some more math!

My pattern repeat is a Multiple of 15 plus a fixed number of 18 stitches. The 18 stitches is only counted one time but the rest of the stitches need to be divisible by 15. For example: 15 + 18 = 33 30 + 18 = 48 45 + 18 = 63 ? + 18 = 214.38* We need to figure out how many multiples of 15 are needed. * We will drop the .38 because we rounded down.

Refined Total Stitches Formula: Total Number of Stitches - Fixed Number of Stitches = ?/15 = Approximate Multiplier

214 - 18 = 196 196/15 = 13.06*

Final Total Stitches Formula: Multiplier x Pattern Repeat Multiple = Pattern Repeat Number of Stitches Pattern Repeat Number of Stitches + Fixed Number of Stitches = Final Total Number Stitches

Now we can determine that 13 x 15 = 195 + 18 = 213 Stitches.

Quick Check Formula: # of stitches to cast on /# stitches per inch = Should Equal Original measurement goal

To do a quick check, let's divide 213 by our original Stitches Per Inch Calculation. We should Get something close to 54 inches, my original goal.

213 / 3.97 = 53.65

Looks great!