Knitting Pi Circles: The Magic of Circular Expansion

Knitting circles can be a fascinating exploration of geometry and stitch increases. One of the most elegant ways to knit a circular shape is using the Pi (π) method, a concept developed by Elizabeth Zimmermann. This method relies on the mathematical principle that the circumference of a circle increases proportionally to its radius.

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The Theory of Pi Circles

The key to understanding a pi circle is that, as the radius doubles, the number of stitches needed to maintain a flat shape must also double. Instead of increasing every round (as in a standard circular knitting method), the Pi method spaces out increases exponentially:

  1. Start with a small number of stitches in the center.

  2. Double the stitch count after a few rounds.

  3. Work twice as many rounds before the next increase.

For example, if you start with 9 stitches. After 3 rounds, double the stitches. After 6 more rounds, double again. After 12 more rounds, double again. Continue doubling the spacing between increases. This results in a beautifully smooth and even circle without puckering or waves.

Knitting from the Inside Out (Center Start)

This is the most common method for pi shawls, coasters, mandala's or circular blankets.

  1. Cast On: Use a circular cast-on, such as Emily Ocker’s cast-on or a simple looped start with magic loop/DPNs.

  2. Increase Rounds: Follow the pi increase formula (doubling stitches at set intervals).

  3. Edge Finish: Once you reach the desired size, bind off loosely or add a decorative border, such as lace or garter stitch.

Sample Pattern (Basic Pi Circle – Inside Out)

  • Cast on 8 stitches.

  • Round 1: Knit all stitches.

  • Round 2: (Kfb) in each stitch (16 stitches).

  • Knit 2 rounds.

  • Round 6: (Kfb) in each stitch (32 stitches).

  • Knit 4 rounds.

  • Round 12: (Kfb) in each stitch (64 stitches).

  • Knit 8 rounds.

  • Continue this pattern, doubling stitch count after twice as many rounds each time.

Knitting from the Outside In (Border Start)

This approach works well for lace shawls or doilies, where the decorative edge is prominent.

  1. Cast On: Begin with a long circular needle and a large number of stitches.

  2. Decrease Rounds: Work decrease rounds at pi intervals, halving the stitch count.

  3. Center Close: Finish with a small number of stitches and cinch them closed.

Sample Pattern (Basic Pi Circle – Outside In)

  • Cast on 576 stitches.

  • Knit 12 rounds.

  • Round 13: (K2tog) across (288 stitches).

  • Knit 6 rounds.

  • Round 20: (K2tog) across (144 stitches).

  • Knit 3 rounds.

  • Round 24: (K2tog) across (72 stitches).

  • Continue decreasing until you have 9 stitches left, then cinch closed.

Examples & Inspirations

Here are some pi circle designs you might enjoy:

  • EZ's Pi Shawl (Classic and adaptable)

  • Laminaria Shawl (Pi-inspired lace)

  • Girasole by Jared Flood (Textured pi blanket)

For images and inspiration, check these sources: