Introduction
Knit it Now Tools
LIVE replay
Knitting Diagonals
Stuff you should know

The Magic Formula

Even if you NEVER intend to chart your own knitting patterns, it is important to understand the basics. The Magic Formula is one of those basics that every knitter should at least be familiar with

In charting knitting patterns, we use this equation for numerous applications.
  • Straight line decreasing and increasing of side seams on skirts, sleeves, slacks, and jackets
  • Multiple increasing or decreasing across a single row of knitting.
  • Placing darts and buttonholes
  • Arranging short row increments for curves
  • Determining the stitches in knitting a slanted line
  • One can determine rows and/or stitches to be increased or decreased WITHIN a definite amount of space.
  • Buttonhole placement, vertical or horizontal, can be situated in exactly balanced spots
  • Short row operations can be determined for shoulder slants, pockets, collars, and all kinds of sideways knitting.
The formal name of this mathematical formula is "The Diophantine Equation". Others also refer to it as "The Diophantine Analysis". The concept was discovered by a Greek mathematician named Diophantus who lived around 250 A.D. He developed this equation which only accepts integral parts. (whole numbers)
In plain language - when using this formula, your answers will be the most even division of one number into another.
Today, doing long division isn't necessary. Use the Knit it Now tools for all of these calculations


Diophantine Calculation

Magic Formula Tools

Magic Formula <span class='reallysmall'>(Sts and rows)</span>

Magic Formula (Sts and rows)

Increase or decrease evenly for perfect shaping. Shorten or lengthen any shaped area of your knitting by entering stitches and rows

Magic Formula <span class='reallysmall'>(Inches)</span>

Magic Formula (Inches)

Increase or decrease evenly for perfect shaping. Shorten or lengthen any shaped area of your knitting by entering inches or cm.
Use the Knit it Now Tools to calculate even increases or decreases for shaping sleeves or any diagonal shaping with the Magic Formula.

Video: Magic Formula (sts/rows)

Video: Magic Formula (measure)

Slope Tool

Slope Tool

Slope Tool

Enter your gauge, width and depth (height) and Knit In Now will produce your line by line instructions for your slopes. Use to calculate shoulder shaping.
Magic formula:
Increase or decrease evenly over more ROWS than STITCHES
Slope formula:
Increase or decrease evenly over more STITCHES than ROWS


The mathematical equation for shaping over more STITCHES and ROWS is not the same as the Magic Formula.
Use this tool for shoulder shaping or any time your diagonal is worked over more stitches than rows.

Not so Magic Formula

Shaping your knitting and getting the increases and decreases JUST RIGHT can be a challenge. If you are altering a pattern or creating your own, guesswork just doesn't cut it.
Let's talk about shaping without adding, subtracting, multiplying or dividing ANY numbers!
Shorten/lengthen sleeves or shaped garments, add shaped shoulders for better fit, plan triangles for interesting shapes and turning corners.
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Links mentioned in the Show

Jodi Raymond Favorite Demo 2 (PDF) Great examples and practice with Magic Formula math

We recommend any books by Kathleen Kinder

Diagonal Shaping DAK
Explore the convex and concave curves formed by grouping shaping instructions

Over Under Shawlette

Magic Formula Stitches and Rows
Magic Formula Inches/CM
Taper Tool

Increasing and Decreasing Techniques

There are many ways to working diagonal shaping on the knitting machine.

From transferring stitches for increases and decreases to working short rows, every machine knitter needs to know multiple techniques.

Increase/Decrease Classroom

Things to Keep in Mind

Easy knitting versus accuracy.

When knitting diagonals, we use the magic formula (Diophantine Calculation) to determine the shaping instructions.

For example. Decrease 1 stitch every 3 rows, 1 stitch every 2 rows.

Variations on these instructions can make a big difference in the shape of your diagonal shaping.

Diagonal Shaping

DAK 8 - Diagonal Shaping