Cross Stitch CalculatorMethodology and Sources
This page lists every formula, constant, default and rounding rule used by the Cross Stitch Calculator tools, with the source of each fact. Method version 1.1, facts last checked 2026-11-14.
Units and rounding
- One inch is exactly 2.54 cm (NIST). All sums run in inches at full precision; centimetres are converted at the end.
- Displayed lengths are rounded half-up to 0.1 in or 0.1 cm. Plain JavaScript rounding mis-rounds some halves, so the site uses its own half-up rounding.
- Stitch counts that must fit a space are rounded down to whole stitches.
- “Buy at least” fabric sizes and skein counts are rounded up, so you never buy short.
Design size and fabric size
stitches per inch = count ÷ over
design width = stitches wide ÷ stitches per inch
fabric width = design width + 2 × margin
Height uses the same lines. “Over” is 1 for Aida and 2 for evenweave or linen stitched over two threads, which you can change. This is the same arithmetic shop calculators use; ours adds centimetres, every count at once and margin presets.
Margin presets
The margin is per side and fully adjustable. Stitching guides commonly give 2 to 3 in (5 to 8 cm) per side. The presets are:
| Preset | Per side | Why |
|---|---|---|
| Frame, no mat | 3 in (7.5 cm) | Framers lace or pin the fabric over a board, which takes about 3 in per side. |
| Frame with a mat | 4 in (10 cm) | A mat covers the edge of the stitching area, so more fabric is needed. |
| Hoop display or pillow | 2 in (5 cm) | Enough fabric to grip in the hoop or sew into a seam. |
| Card or ornament | 1 in (2.5 cm) | Small finishes are trimmed close; 1 in holds the work while stitching. |
| No margin (design only) | 0 in (0 cm) | Design size only, for checking a chart. |
Stitch count and largest design
stitches = ⌊ length (in) × count ÷ over ⌋
largest design = ⌊ (fabric length − 2 × margin) × count ÷ over ⌋
Count conversion
size ratio = (old count ÷ old over) ÷ (new count ÷ new over)
A ratio below 1 means the design gets smaller. The converter also lists the common fabrics with the same stitches per inch as the original.
Hoop and frame size
hoop ≥ √(design width² + design height²) + 2 × space
frame: (width + 2 × space) ≤ one side and (height + 2 × space) ≤ the other, either way round
fabric for a hoop finish = hoop + 2 × wrap
- A rectangle fits inside a circle only if its diagonal fits, so the hoop check uses the diagonal.
- Round hoops checked: 3, 4, 5, 6, 7, 8, 9, 10, 12, 14 in. Frames checked: 6 × 6, 8 × 8, 11 × 11, 11 × 17, 14 × 14, 17 × 17 in, the Q-Snap range sold at retailers such as 123Stitch. Sizes are nominal; the inner opening can be slightly smaller.
- Defaults: 0.5 in of space between the design and the hoop, and 2 in of fabric to wrap behind the hoop. Both are our defaults and can be changed.
Time to finish
stitches = width × height × area stitched (%)
hours = (stitches − stitches done) ÷ stitches per hour
stitching days = ⌈hours ÷ hours per day⌉ · calendar days = ⌈stitching days × 7 ÷ days per week⌉
The speed field starts at an example of 100 stitches an hour; it is not an average, because speeds vary widely between stitchers and designs. The built-in timer divides the stitches you made by the time it ran to give your own speed. Finish dates are counted in whole days from the start date.
Floss model
Floss estimates come from the thread path of each stitch, not from a single “stitches per skein” figure, because published figures disagree widely: for 14-count Aida with two strands they range from a few hundred to almost 2,000 full crosses per skein.
stitch side s = 2.54 × over ÷ count (cm)
full cross = (2√2 + 2) × s · half stitch = (√2 + 1) × s · backstitch = 3 × s per stitch length
working thread = path × (1 + allowance)
skeins = Σ (stitches × working thread × strands) ÷ (6 × 800 cm), rounded up per colour
- Thread path. A full cross runs two diagonals across the front (2√2 × s) and two short verticals on the back (2 × s), the path of stitching in rows. A half stitch is half of that. A backstitch shows one stitch length on the front and runs two on the back.
- Allowance, default 50%. The path above ignores the thread that passes through the fabric, starting and ending tails, and travel between stitches. The default makes one skein on 14-count Aida with two strands cover about 1,826 full crosses, inside the range of published planning figures. You can change it on the floss calculator.
- Skein. DMC six-strand floss (Mouliné Spécial, article 117): 8 m (8.7 yd) of six strands, per DMC. That is 4,800 cm of single strand per skein.
- Worked check. On 14-count, s = 0.181 cm, so a full cross is 0.876 cm before the allowance and 1.314 cm after it. With two strands, 4,800 ÷ (1.314 × 2) ≈ 1,826 stitches per skein.
- Limits. The model does not know your stitching method, tension or how far you carry thread. Treat results as a planning estimate and buy an extra skein for large areas.
Strands and needle sizes
Only advice a named source states is shown; anything else reads “Not stated by our sources”.
| Fabric | Strands | Source | Needle | Source |
|---|---|---|---|---|
| 11-count, over one | 3–4 | Colonial Needle | — | — |
| 14-count, over one | 2 | Colonial Needle | Size 24 (26 also used) | Lindy Stitches |
| 16-count, over one | 2 | Colonial Needle | Size 26 | Lindy Stitches |
| 18-count, over one | 1–2 | Colonial Needle | Size 28 | Lindy Stitches |
| 20-count, over one | 1 | Colonial Needle | — | — |
| 25-count, over one | 1 | Colonial Needle | — | — |
| 25-count, over two | 2 | Colonial Needle | — | — |
| 28-count, over two | 1–2 | Colonial Needle | Size 24 | Lindy Stitches |
| 32-count, over two | 1–2 | Colonial Needle | Size 26 | Lindy Stitches |
| 36-count, over two | — | — | Size 28 | Lindy Stitches |
How the tools are tested
Every formula has an automated test with hand-worked values, run before each release. For example, 140 × 100 stitches on 14-count Aida with 3 in margins must give a 10.0 × 7.1 in design on 16.0 × 13.1 in (40.6 × 33.4 cm) of fabric, and 28-count over two must equal 14-count Aida exactly. The same code produces the result in the page HTML and the live result as you type, so the two cannot disagree.
How these pages are made
We use AI tools to help write code and draft text. Material facts such as skein length, strands and needle sizes are taken only from the sources listed below and checked on the date shown. Formulas are checked by the automated tests above. When a fact or formula changes we update the page, raise the method version and record it in the changelog; dates change only when the content does.
The formulas, defaults and sources are maintained by Fahad Shoaib, the site owner, who also handles correction reports.
Sources
- NIST unit conversion (1 inch = 2.54 cm exactly), checked 2026-11-14.
- DMC, Mouliné Spécial six-strand floss (sold in 8 m / 8.7 yd skeins), checked 2026-11-14.
- Fat Quarter Shop, beginner's guide to cross stitch floss and needles, checked 2026-11-14.
- Colonial Needle, how many strands of embroidery floss to use, checked 2026-11-14.
- Lindy Stitches, what size needle do I need, checked 2026-11-14.
- Maggie Frames, what size embroidery hoop do I need, checked 2026-11-14.
- 123Stitch, Q-Snap frame listings (6 × 6, 8 × 8, 11 × 17, 17 × 17 in), checked 2026-11-14.
- Willow Fabrics, what is evenweave fabric: Jobelan, Lugana and Murano compared, checked 2026-11-14.
- Herrschners, cross stitch fabrics 101, checked 2026-11-14.
- Stitched Modern, how to choose fabric for cross stitch, checked 2026-11-14.
Changelog
- , version 1.1: Added the hoop and frame size formulas and the time-to-finish formula.
- , version 1.0: First version: design size, fabric size, stitch count, count converter and floss formulas.
Found an error? Tell us and we will check it against the sources and correct it.