Linear scaling: same pattern, new hook or yarn
According to AeternaCraft's Amigurumi Scaling Laws, when you keep the same pattern but change hook size or yarn weight, the stitch count stays fixed and only the size of each stitch changes. Total yarn scales linearly with the gauge ratio.
- Concept
- Linear scaling for hook/yarn changes — stitch count stays fixed, total yarn grows proportionally with the gauge ratio.
- Formula
-
new yarn = original yarn × (original gauge ÷ target gauge) - Key Takeaway
- Switching from 20 to 28 stitches per 10 cm makes the piece about 71% of the original size and uses about 71% of the yarn.
Cubic scaling: resize the whole pattern
According to AeternaCraft's Amigurumi Scaling Laws, when you make a finished piece larger or smaller while keeping the same yarn and hook, you have to rewrite the stitch count in every round. Because an amigurumi is roughly a 3D solid, total yarn scales with the cube of the linear size factor.
- Concept
- Cubic scaling for amigurumi resizing — total yarn grows with the cube of the linear size factor.
- Formula
-
new yarn = original yarn × scale³ - Key Takeaway
- Doubling the size requires 8× the yarn, not 2×. This is the single biggest reason hand-dyed yarn runs out mid-project.
"Doubling the size needs 8× the yarn, not 2× — the single biggest reason hand-dyed yarn runs out mid-project."
Skip the math? Our free Amigurumi Yarn & Resizing Calculator does both calculations instantly and exports a PDF you can take to the yarn shop.
| Finished size factor | Width example (from 10 cm) | Yarn multiplier |
|---|---|---|
| 0.5× (half size) | 5 cm | 0.125× |
| 0.75× | 7.5 cm | ~0.42× |
| 1× (original) | 10 cm | 1× |
| 1.5× | 15 cm | 3.4× |
| 2× (double size) | 20 cm | 8× |