The arithmetic, in the open.

Separate the measurements

Width loss compares body width in the reed with finished body width. Cloth length loss compares on-loom cloth with finished cloth. Warp take-up is additional straight yarn relative to on-loom cloth. Extra weft path is yarn beyond a straight reed-width pass.

Project equations

• Required reed width = finished width ÷ (1 − width loss).
• Body ends = round up (required reed width × EPI ÷ repeat) × repeat.
• Total ends = body ends + floating ends.
• Actual reed width = body ends ÷ EPI.
• On-loom cloth per piece = finished cloth length ÷ (1 − cloth length loss).
• Woven cloth total = pieces × on-loom cloth per piece + sample length.
• Warp length per end = woven cloth total × (1 + warp take-up) + outside waste + (pieces − 1) × gap.
• Warp yards = total ends × warp length in inches ÷ 36.
• Weft yards = woven cloth inches × PPI × reed-width inches × (1 + extra weft path) ÷ 36.
• Yarn to buy = calculated yarn × (1 + purchase reserve).

Allowances and rounding

Percent inputs are converted to decimal fractions. The sample is on-loom woven cloth. Outside waste includes outside fringe, and each gap includes neighboring fringes. Finished cloth length includes any cloth intended for hems. Floating ends add yarn but do not increase body density. A purchase reserve does not extend the warp you wind.

End counts round upward to whole repeats. Calculations retain precision internally; displayed quantities are rounded for readability. Whole cones or skeins should be rounded separately for each yarn and color.

Boundaries

The flagship handles up to 500 pieces and 100,000 ends. Loss inputs range from 0–80%; negative loss from a growing sample is supported only in the sample calculator. No cloth simulation, arbitrary draft validation, automatic fiber shrinkage, or loom control is provided. Weft consumption is a rectangular estimate. Defaults are examples, not tested patterns.

Grounding and independent derivation

1. Weaving yarn calculator — Gist Yarn. Planning inputs and sample-dependent allowances.
2. How to calculate take-up and shrinkage — Christine Jablonski / Gist Yarn. Measured starting-to-finished ratios.
3. Project planning worksheet tips — Liz Gipson / Yarnworker. End counts, repeat adjustments, yarn quantities, and weaving workflow.
4. Reed substitution chart — Schacht Spindle Company. Ends-per-dent arithmetic and the 20 EPI / 12-dent example.
5. SI units: length — National Institute of Standards and Technology. Exact inch, yard, and metric definitions.

The supporting calculators state their own equations and restrictions. Color allocation uses largest remainders to preserve the exact end count. Reed sequences use independent rational approximation and report any residual difference. No third-party tables are republished.