Spread Interior Warp Ends Across a Reed Without Losing Remainder Ends — Free
A fractional ends-per-dent average is not a threading plan. Keep every remainder end in an explicit integer occupancy sequence, with selvedges separated, before checking a reed plan with the weaver responsible for it.
The proof surface
Knitting gauge tools resize stitches. This ladder emits a bounded interior reed-occupancy pattern, preserving integer ends and distributing remainder positions by a declared floor-difference rule. It does not choose yarn sett, draft or selvedge treatment.
InputWarp plan | total warp ends including selvedges | interior dents available; selvedge ends excluded from this interior plan (both edges combined)
Rare deviceKnitting gauge tools resize stitches. This ladder emits a bounded interior reed-occupancy pattern, preserving integer ends and distributing remainder positions by a declared floor-difference rule. It does not choose yarn sett, draft or selvedge treatment.
Output artifactEmpty dents in the declared interior patterns with row-by-row context
Cost$0 local calculation · no card, paid key, subscription or signup · proposed filing price is not for sale
Sample, not your facts: Illustrative inputs: Pine scarf | 84 | 20; Wren sampler | 19 | 20. Selvedge ends excluded from this interior plan (both edges combined) = 4. Empty dents in the declared interior patterns: 5 empty interior dents. All records are invented.
Before using the reed-pattern ladder
The plan assumes an ordered sequence of up to two hundred usable interior dents. Exclude the combined selvedge end count first and keep the selvedge placement in a separate verified plan. The remaining ends are spread as evenly as this specific arithmetic rule permits: occupancy at position i is floor((i+1)×ends/dents) minus floor(i×ends/dents), starting at i=0. Every occupancy is a whole number, neighboring sizes differ by at most one, and the total equals interior ends. This does not establish a suitable sett, tension or weave structure. A pattern with empty dents is explicitly visible, not automatically wrong. Different starting phases or a loom-specific threading plan can place remainders differently while preserving the same total.
Why the flat version breaks
Rounding the average in every dent
An average of fifteen ends across twenty dents is 0.75, but rounding every position to one would add five ends. The explicit sequence allocates fifteen ones and five zeros, preserving the count. Other densities likewise need their remainder ends placed rather than silently lost or created.
Subtracting a per-edge exclusion as a combined count
The setting is both selvedges combined. Confusing four per edge with four total changes interior count by four. Confirm the original plan and keep edge placement separate; the ladder deliberately does not guess which dents should carry selvedges.
Treating an even schedule as a sett recommendation
Integer distribution does not evaluate yarn, structure, shrinkage or tension. A technically balanced count can still produce unsuitable cloth. Have the responsible weaver review the actual draft rather than presenting this ladder as a universal threading or density prescription.
How to work the reed-pattern ladder
Confirm which ends and dents belong to the interior
Ask the weaver to distinguish selvedge ends from the interior and identify usable dent positions. Enter a combined selvedge exclusion, not a per-edge count that would be subtracted twice. A total warp count includes those excluded ends; the interior dent count does not include their separate positions.
Enter whole counts for each alternative plan
Use a positive whole total warp count and one through two hundred interior dents. The total must be at least the supplied exclusion. Labels identify alternative warps, not simultaneous segments to be silently joined. The app has no reed number, yarn diameter or loom specification, and it cannot infer any of them from the resulting average.
Inspect the exact occupancy sequence
Subtract selvedges to obtain interior ends, then compute the floor-difference occupancy at each dent. The reading lists all positions, the low and high occupancy sizes, their counts and any zeros. Summing the emitted sequence must recover the interior end count exactly. The remainder positions are part of the declared algorithm, not omitted rounding errors.
Review the pattern against the actual draft
Compare the sequence with the yarn, structure and loom plan before threading. Ask an experienced weaver about sett, tension and selvedges. This evenly distributed arithmetic may not be the right artistic or structural choice. Save the convention with the plan so a later revision does not look like a physical instruction from an unverified density calculation.
What the reed-pattern ladder separates
Question
Before
Inspect this instead
Rounding the average in every dent
An average of fifteen ends across twenty dents is 0.75, but rounding every position to one would add five ends. The explicit sequence allocates fifteen ones and five zeros, preserving the count. Other densities likewise need their remainder ends placed rather than silently lost or created.
Enter whole counts for each alternative plan
Subtracting a per-edge exclusion as a combined count
The setting is both selvedges combined. Confusing four per edge with four total changes interior count by four. Confirm the original plan and keep edge placement separate; the ladder deliberately does not guess which dents should carry selvedges.
Inspect the exact occupancy sequence
Treating an even schedule as a sett recommendation
Integer distribution does not evaluate yarn, structure, shrinkage or tension. A technically balanced count can still produce unsuitable cloth. Have the responsible weaver review the actual draft rather than presenting this ladder as a universal threading or density prescription.
Review the pattern against the actual draft
This reed-pattern ladder replaces a manual count or calculation, not source verification or the responsible person’s review.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
Interior-end distribution arithmetic only, not a sett, loom-safety or cloth-performance recommendation. Confirm total/selvedge counts and review the emitted sequence with an experienced weaver against the actual yarn, structure and loom plan.
Data note: The reed-pattern ladder processes Warp plan | total warp ends including selvedges | interior dents available locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.
Go deeper: the companion app files the same reading as a climbing rung ladder
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the reed-pattern ladder reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
The reed-pattern ladder answer stays complete for free. The proposed $4 one-time filing layer adds row CSV, print and five local reading summaries, not hidden answers. Checkout is unavailable; the article demo remains unlimited.
Interior-end distribution arithmetic only, not a sett, loom-safety or cloth-performance recommendation. Confirm total/selvedge counts and review the emitted sequence with an experienced weaver against the actual yarn, structure and loom plan.
What this is built on
Method: Subtract selvedges to obtain interior ends, then compute the floor-difference occupancy at each dent. The reading lists all positions, the low and high occupancy sizes, their counts and any zeros. Summing the emitted sequence must recover the interior end count exactly. The remainder positions are part of the declared algorithm, not omitted rounding errors.
All sample records, dates, quantities and labels are invented. No outside policy, contract, rate, clock offset, measurement or accessibility standard is represented as verified.
Google’s official pricing documentation, fetched 2026-10-01, says AI Studio is free in available regions. Optional formatting may require a Google account; manual local entry requires none. Limits can change and free-tier content may be used to improve products. Do not send private records.
Before: a fractional average lost remainder ends during threading. After: each interior dent has a counted whole occupancy and selvedges remain separate.
Three worked readings, with different inputs
Sample A — typical inputs
Pine scarf | 84 | 20
Wren sampler | 19 | 20
Setting: Selvedge ends excluded from this interior plan (both edges combined) = 4. Expected summary: 5 empty interior dents.
Pine has eighty interior ends after excluding four selvedge ends; twenty dents each receive four. Wren has fifteen interior ends for twenty dents. The declared floor-difference pattern places fifteen single ends and five empty dents, totaling all fifteen ends. The summary reports five empty interior dents across both plans, not five missing warp ends. Selvedge placement is explicitly outside the pattern.
Sample B — changed plan
Oak band | 44 | 10
Narrow sampler | 7 | 10
Setting: Selvedge ends excluded from this interior plan (both edges combined) = 4. Expected summary: 7 empty interior dents.
Oak's forty interior ends fit four per dent across ten dents. Narrow has three interior ends after the same four-end selvedge exclusion. Its ten-position schedule contains three occupied dents and seven zeros, so the summary is seven empty dents. Empty positions may be an intentional spacing choice, but this arithmetic does not determine whether that density suits the yarn or structure.
Sample C — boundary convention
Selvedge-only boundary | 4 | 6
Setting: Selvedge ends excluded from this interior plan (both edges combined) = 4. Expected summary: 6 empty interior dents.
Total ends equal the excluded selvedge count, leaving no interior ends. All six interior dents are zero in the emitted schedule, so six are reported empty. The boundary is a mass-count identity, not a usable cloth prescription. A total below the exclusion would be rejected rather than inventing negative interior ends or placing selvedges into this separate interior schedule.
Optional AI formatting, never the calculation
Manual entry completes this reed-pattern ladder for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a reed-pattern ladder. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string"]}], "setting": "string"}. The columns are Warp plan | total warp ends including selvedges | interior dents available; the setting is Selvedge ends excluded from this interior plan (both edges combined). Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.