Knitting Needs Mathematics

Whether you are designing projects, following pattern instructions, or adapting a vintage pattern, math skills are an essential part of knitting. Maybe you get an inkling that the stitch numbers are inaccurate in the instructions? How in the world do I figure out the number of stitches to cast on to achieve a certain width? How do I shape a raglan and achieve the required armhole depth? How do I arrange a pattern with multiples across the width of a knit fabric? And how do I figure out how many skeins of yarn I need to make a sweater that requires 1600 metres of chunky yarn? These are just some of the questions a knitter will have to answer, and invariably they require basic math calculations to resolve. Let’s delve into the key aspects of knitting where math is essential. I won’t discuss the detailed math for the broad range of knitting techniques, but only to point out that math is the basis of knitting.

Measurement Systems

I’m sure you’re familiar with the two systems of measurements, metric and imperial. North Americans tend towards the imperial system, measuring in inches versus centimeters of the metric system. Whichever system you choose to work in, be consistent throughout the project by using one or the other. There are differences between the two systems, that will affect the project’s measurements if you switch between them while knitting a project. I draw my schematics in inches, but I use math to convert between metric and imperial. Regardless of which system you choose to work in, the math is the same. Good pattern instructions give all measurements in both systems, making it easier for the knitter.

Basic Conversion Factors

Imperial to Metric
inches(in) x 2.5 = centimeters(cm)
yards(yds) x 0.9 = meters(m)
ounces(oz) x 28 = grams(g)

Metric to Imperial
centimeters(cm) x 0.4 = inches(in)
meters(m) x 1.1 = yards(yds)
grams(g) x 0.035 = ounces(oz)


This is the most important ratio of all in knitting. Gauge is the number of stitches and rows per inch/centimeter of knit fabric. The gauge is calculated from a test swatch, and is the basis of designing and writing pattern instructions. The resulting gauge determines the finished size or measurements of a project. This means the number of stitches and rows per in/cm are used to figure out stitch and row counts for the various sections of your knit pieces. The math involves multiplication to determine how many stitches and rows are required to achieve the desired measurements as in the sample schematic below.

From Knitwear Design Workshop by Shirley Paden (an excellent book)

And it goes without saying, when following pattern instructions knitters must obtain the same gauge as in the instructions to achieve the correct measurements of the design. This involves simple math with possible adjustments to the instructions. 

Note: Remember that in knitting you only work in whole numbers. For most calculations the numbers need to be rounded up or down.

Math Checking Pattern Instructions

On occasion you may find a mistake in the measurements, or with the stitch and row counts of a pattern. A math error is really one of the most common mistakes found in pattern instructions, and is usually a clerical error that is easily remedied with a math check. Finding a math error doesn’t mean that the design can’t successfully be made. By applying some basic math calculations, you can recheck that the numbers in the instructions are accurate. For example, you may find that the stitch number doesn’t jive with the width measurement. Simply take width measurement for the piece divided by the stitch gauge (number of stitches per in/cm) to check that the number of stitches you obtain is the same as in the instructions.

I often recheck stitch and row numbers for shoulders, or other areas that are a result of shaping to see that they are correct and representative of the measurements.

Yarn Amounts

Determining how much yarn to purchase for a project requires simple math to estimate quantities. When substituting a different yarn for the one asked for in the instructions, it’s important that the amount of yarn is calculated based on the meterage/yardage required, and not the amount in grams/ounces.

Shaping Knit Pieces

Garment construction requires calculations to shape areas such as sleeves, raglans, yokes, necklines and waistlines. These garment sections all require either increasing or decreasing stitches worked within a certain number of rows, to obtain the length measurement for the section, hence the stitch and row gauge is used in the math calculations. For example, a classic sleeve has increases made within a specific length measurement in order to reach the required number of stitches at the armhole.

Any increases or decreases need to be evenly distributed across a row, such as in a ribbed border to reach the correct number of stitches for the body of a garment. In addition, picking up stitches and determining buttonhole placement also need to be evenly distributed along the edge to be worked.

Check out these previous posts for the appropriate math calculations required for a variety of knitting topics: How to Figure Out Increase and Decrease Placement – When Adjusting Sleeve Length and Cap Shaping; How much yarn do I need for my project?; How to Mark Your Project for Buttonhole Placement; Tips to Adapting Vintage Knitting Pattern; and The Why and How of Test Swatching.

The above are the main aspects of knitting requiring simple math skills. Even if you dislike mathematics, just knowing how to calculate stitch and row gauge, will go a long way to helping you understand pattern instructions, and successfully complete knit projects. Just because you only follow instructions doesn’t mean that you won’t have to deal with any underlying math problems. With some practice, you’ll be able to design or adapt instructions to your liking. It’s not that difficult.