Hello! Welcome to the third lesson in our module on the mathematics of flat circles.
In our last two lessons, we established the core architectural principles of a circular design. We learned why a flat circle requires a constant number of increases per round (related to Pi and stitch height) and that this number is determined by the stitch you choose for your first round. This starting stitch count also defines the number of symmetrical "segments" your doily will have.
Today, we move from the "what" and "why" to the "how." We'll answer the question: Exactly where do I place the increases in each round? You will learn to calculate the specific, repeatable formula for distributing increases to create a perfectly flat circle using single, half-double, and double crochet stitches. Mastering this is the final step in understanding the mathematical engine that drives circular growth, and it's a crucial skill for drafting your own patterns.
The Universal Formula for Placing Increases
We know that for a circle starting with X stitches, we need to add X more stitches in every subsequent round. But how do we space them? Thankfully, there's a simple, universal rule.
An excellent article from B Hooked Crochet explains this principle clearly.
How to Make a Perfectly Flat Crochet Circle + ...
The article 'How to Make a Perfectly Flat Crochet Circle' lays out the fundamental rule for distributing increases.
Please read the short section titled 'Evenly Space Increases to Crochet a Flat Circle'. Focus on the rule provided in bold text about how the number of stitches between increases changes with each round.
As the article explains, the rule is: For each round after round two, the number of stitches between each increase grows by one.
Let's break this down into a generic formula, where X is your starting stitch count and "inc" means to work two stitches into the same stitch from the round below.
- Round 1: Work
Xstitches into your starting ring. (Total:Xsts) - Round 2: Work an increase in every stitch. Repeat
Xtimes. (Total:2Xsts) - Round 3: Repeat
(1 stitch, 1 inc)Xtimes. (Total:3Xsts) - Round 4: Repeat
(2 stitches, 1 inc)Xtimes. (Total:4Xsts) - Round 5: Repeat
(3 stitches, 1 inc)Xtimes. (Total:5Xsts)
Do you see the pattern? For any given round n (where n > 2), the formula is simply:
Repeat (n-2 stitches, 1 inc) X times.
This elegant formula is the key to creating the basic structure of any flat circle, no matter the stitch type.
Applying the Formula to Specific Stitches
Now, let's apply this universal formula to our three main stitches by plugging in their standard starting counts (X).
A Note on "Magic Numbers"
You may notice that different resources suggest slightly different starting numbers. For example, some say to start a double crochet circle with 10 stitches, while others say 12. This is because the "perfect" number depends on your unique stitch geometry—the ratio of your stitch's height to its width—which is affected by your tension, hook, and yarn.
- Theory (from our videos): Based on pure geometry, the ideal numbers are often stated as SC=6, HDC=9, DC=12.
- Practice: Many designers use common "rules of thumb" like SC=6, HDC=8, DC=10 or 12.
The most important thing is consistency. The number you start with is the number you must increase by in every round. For our examples, we will use the most common values found in vintage and modern doily design.
1. Single Crochet (sc) Circle
- Standard starting count
X = 6. - Round 3:
(3-2 sc, inc)repeated 6 times ->(1 sc, inc)x 6. (18 sts total) - Round 4:
(4-2 sc, inc)repeated 6 times ->(2 sc, inc)x 6. (24 sts total) - Round 5:
(5-2 sc, inc)repeated 6 times ->(3 sc, inc)x 6. (30 sts total)
2. Half Double Crochet (hdc) Circle
- Common starting count
X = 8. - Round 3:
(3-2 hdc, inc)repeated 8 times ->(1 hdc, inc)x 8. (24 sts total) - Round 4:
(4-2 hdc, inc)repeated 8 times ->(2 hdc, inc)x 8. (32 sts total) - Round 5:
(5-2 hdc, inc)repeated 8 times ->(3 hdc, inc)x 8. (40 sts total)
3. Double Crochet (dc) Circle
- Common starting count
X = 12. - Round 3:
(3-2 dc, inc)repeated 12 times ->(1 dc, inc)x 12. (36 sts total) - Round 4:
(4-2 dc, inc)repeated 12 times ->(2 dc, inc)x 12. (48 sts total) - Round 5:
(5-2 dc, inc)repeated 12 times ->(3 dc, inc)x 12. (60 sts total)
Test your understanding!
You are designing the center of a doily using double crochet (dc) stitches, and you started with 12 dc in your first round. What would the written instruction be for Round 7? What is the final stitch count for that round?
Show answer
The formula for Round n is (n-2 stitches, inc). For Round 7, that's (7-2 stitches, inc), which is (5 stitches, inc).
Since you started with 12 dc, you will repeat this pattern 12 times.
Instruction: [5 dc, 2 dc in next st] repeat 12 times.
Final Stitch Count: 7 * 12 = 84 stitches.
To see these formulas in the context of full patterns, the following resource provides clear, round-by-round instructions for all three stitch types.
Flat Circles in Single, Half Double, and Double Crochet
The article 'Flat Circles in Single, Half Double, and Double Crochet' from Jessie at Home provides excellent reference patterns that demonstrate these increase formulas in action.
Please review the written patterns provided for the Single Crochet, Half Double Crochet, and Double Crochet flat circles. For each one, notice how the number of stitches between the increases (the '2 sc in next st' part) grows by one each round, matching the formula we just discussed.
Refining the Circle: From Polygon to Perfect Round
If you follow the increase formula exactly as written—for example, [4 sc, inc] 6 times—you might notice something interesting. Your circle isn't perfectly round. It's starting to look like a hexagon. This happens because the increases are "stacking" on top of each other in each round, creating subtle corners.
To create a truly round circle, we need to make one small adjustment: staggering the increases.
The following video gives a great visual explanation of this problem and its solution.
The Secret to Making a Flat Circle with Single Crochet
In 'The Secret to Making a Flat Circle,' the presenter clearly demonstrates why stacking increases creates a hexagon and how to avoid it.
Please watch from 05:52 to 09:06. Pay close attention to the visual comparison between the hexagonal piece and the circular piece. Notice how she breaks up the pattern on some rounds to move the increase point.
The principle of staggering is simple: on some rounds (typically the even-numbered ones), you break up the first repeat.
- Standard Round 4 (sc):
[2 sc, inc]repeated 6 times. - Staggered Round 4 (sc):
1 sc,inc, then[2 sc, inc]5 times, then1 scin the last stitch.
You've still worked a total of 6 increases and the same number of single crochet stitches, but you've shifted the start/end point so the increase locations are offset from the round below. This is all it takes to smooth out the corners.
This chart is a wonderful visual reference for how staggered increases work, perfect for your pen-and-paper drafting process.
If you revisit the "Jessie at Home" patterns, you'll see that she has already built this staggering technique right into her instructions, making them a best-practice model to follow.
Conclusion
You now have a complete, practical understanding of the formulas that govern a flat crochet circle. This knowledge frees you from being dependent on patterns and empowers you to build the foundational canvas for your own designs.
Key Takeaways:
- The universal increase formula for round
nis(n-2 stitches, 1 inc), repeatedXtimes (whereXis your starting stitch count). - You can apply this formula to single crochet (X=6), half-double crochet (X=8), and double crochet (X=12) to calculate the pattern for any round.
- Placing increases in the same spot each round creates a polygon (hexagon, octagon, etc.).
- Staggering the increases by splitting the first repeat on alternate rounds breaks up the corners and creates a true circle.
In our next and final lesson of this module, we will explore troubleshooting. We'll learn to diagnose the visual signs of "ruffling" (too many increases) and "cupping" (too few), connecting these common problems back to the math we've just mastered. This will give you the skills to not only draft a circle correctly but also to fix it when it goes wrong.