How the Remainder Math Works (Formulas)
When dividing stitches across a row or round, exact whole divisions rarely happen in real patterns. For instance, when increasing 7 stitches across 43 stitches:
1. Quotient & Remainder Formulation
q = Floor(S_start ÷ Δ_change)r = S_start mod Δ_change
Here,
q represents the base spacing interval, while r is the remainder stitches that must be interleaved across the row.
2. Bresenham Discrete Symmetrical Distribution
If remainder stitches were grouped at either edge, your fabric would pull and bias asymmetrically. AeternaCraft's algorithm uses Bresenham line error accumulation to interleave larger groups:
For each interval i from 0 to Δ-1: acc += r If acc >= Δ: use (q) plain sts + inc; acc -= Δ Else: use (q - 1) plain sts + inc 3. Symmetrical Decrease Row Math
S_plain = S_start - (2 × Δ_decrease)q_dec = Floor(S_plain ÷ Δ_decrease)r_dec = S_plain mod Δ_decrease Because each decrease merges 2 stitches into 1, we isolate the plain stitches first to ensure decreases never overlap or buckle.
Standard Circular Rounds Expansion Reference Table
The geometric gold standard for flat crochet circles (Amigurumi heads, top-down beanies, mandalas) expanding by 6 stitches per round:
| Round # | Starting Count | Pattern Instruction Formula | Stitches Added | End Stitch Count |
|---|---|---|---|---|
| Round 1 | Magic Ring | 6 sc into magic ring | +6 | 6 sts |
| Round 2 | 6 sts | [2 sc in each st] × 6 (all inc) | +6 | 12 sts |
| Round 3 | 12 sts | [sc 1, 2 sc in next st] × 6 | +6 | 18 sts |
| Round 4 | 18 sts | [sc 2, 2 sc in next st] × 6 | +6 | 24 sts |
| Round 5 | 24 sts | [sc 3, 2 sc in next st] × 6 | +6 | 30 sts |
| Round 6 | 30 sts | [sc 4, 2 sc in next st] × 6 | +6 | 36 sts |
| Round 7 | 36 sts | [sc 5, 2 sc in next st] × 6 | +6 | 42 sts |
| Round 8 | 42 sts | [sc 6, 2 sc in next st] × 6 | +6 | 48 sts |
| Round 9 | 48 sts | [sc 7, 2 sc in next st] × 6 | +6 | 54 sts |
| Round 10 | 54 sts | [sc 8, 2 sc in next st] × 6 | +6 | 60 sts |
Frequently Asked Questions
- How do you increase stitches evenly across a crochet row?
- Divide your starting stitch count by the number of increases to find the base spacing interval and remainder. For instance, if you have 47 stitches and need 6 increases: 47 ÷ 6 = 7 remainder 5. You will work 5 intervals of 8 stitches ([sc 7, inc]) and 1 interval of 7 stitches ([sc 6, inc]), interleaved symmetrically.
- Why do crochet patterns say "increase evenly spaced" instead of writing out the row?
- Pattern designers grade multi-size garments (XS through 5XL). Rather than writing 6 separate pages of complex remainder math for every individual size, designers instruct the maker to "increase X stitches evenly" across the waistband, sleeve, or yoke.
- How do you decrease evenly without creating a visible bulge?
- Distribute decreases symmetrically across the row using standard invisible decreases (sc2tog). Staggering your decreases prevents consecutive gathered stitches that cause puckering or uneven fabric tension.
- Does this calculator work for knitting as well as crochet?
- Yes! The mathematical distribution of stitches across an interval is identical in knitting and crochet. In knitting, an increase is typically M1 (make 1) or kfb, while a decrease is k2tog or ssk.
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