Jump to a calculator 618 tools
Yarn Spinning & Preparation
Twist Multiplier to TPI & TPM Calculator
Twist multiplier is count-independent; TPI is not. Set the multiplier, read the machine setting.
Turns per Inch
— TPI
TM x square root of the English count
Derived Twist Metrics
- Turns per Metre
- — TPM
- Tex Twist Factor
- — alpha
- Surface Twist Angle
- — deg
- Estimated Yarn Diameter
- — mm
Typical multipliers: 3.0-3.6 for weft and knitting, 3.8-4.5 for warp, above 5.0 for crepe. Twist angles beyond about 25 degrees begin to cost tenacity.
Using this calculator
About the Twist Multiplier to TPI & TPM Calculator
The formula
This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.
tpi = twistMultiplier x sqrt(yarnNe)The twist multiplier exists because the twist a yarn needs scales with the square root of its count. Quoting TM instead of TPI lets one number describe the same twist hardness across a whole count range.
tpm = tpi / 0.0254 tex = 590.5 / yarnNe alphaTex = tpm x sqrt(tex)Alpha-tex is the same idea expressed in the tex system, and it is what an ISO specification will ask for.
d = 1 / (28 x sqrt(yarnNe)) inch twistAngle = arctan(pi x d x tpi)A surface fibre follows a helix. Unroll one turn and it forms a right triangle whose base is the yarn circumference and whose height is the distance between turns — the angle of that triangle is the twist angle.
| Symbol | Stands for | Unit |
|---|---|---|
twistMultiplier | Twist Multiplier (TM / alpha-e) | TM |
yarnNe | Yarn Count | Ne |
tpi | Turns per Inch | TPI |
tpm | Turns per Metre | TPM |
alphaTex | Tex Twist Factor | alpha |
twistAngle | Surface Twist Angle | deg |
yarnDiameter | Estimated Yarn Diameter | mm |
How the result is derived
Step by step, from the values you type to the figure on screen.
- The twist multiplier is scaled by the square root of the count to give turns per inch, the number the ring frame is actually set to.
- Turns per inch are converted to turns per metre for metric specification and for the alpha-tex calculation.
- The count is converted to tex so the twist factor can be restated in the tex system, where alpha-tex replaces the English twist multiplier.
- Yarn diameter is estimated from the conventional cotton relationship d = 1 / (28 sqrt(Ne)) inches — the same 28 that appears in cover factor, and for the same geometric reason.
- The twist angle follows from the diameter and the turns per inch. It is the honest measure of twist hardness, because it accounts for yarn thickness where TPI alone does not.
What each input means
Where to read each value on the floor, the unit it must be in, and the range the tool accepts.
| Input | Unit | Accepted range | Default | What it means |
|---|---|---|---|---|
| Twist Multiplier (TM / alpha-e) | TM | 1 to 8 TM | 3.8 | |
| Yarn Count | Ne | 1 to 300 Ne | 40 |
What the tool returns
The headline figure and every supporting value it is built from.
| Output | Unit | What it tells you |
|---|---|---|
| Turns per Inch (headline result) | TPI | TM x square root of the English count |
| Turns per Metre | TPM | |
| Tex Twist Factor | alpha | |
| Surface Twist Angle | deg | |
| Estimated Yarn Diameter | mm |
Worked example
Given
- Twist multiplier
- 3.8 TM
- Yarn count
- 40 Ne
Substituting
tpi = 3.8 x sqrt(40) = 3.8 x 6.3246 = 24.03tpm = 24.03 / 0.0254 = 946.19tex = 590.5 / 40 = 14.76 ; alphaTex = 946.19 x sqrt(14.76) = 3635d = 1 / (28 x 6.3246) = 0.005647 inch = 0.1434 mmangle = arctan(pi x 0.005647 x 24.03) = 23.09 degreesAnswer
- Turns per inch
- 24.03 TPI
- Turns per metre
- 946.19 TPM
- Alpha-tex
- 3635.46
- Twist angle
- 23.09 degrees
- Yarn diameter
- 0.1434 mm
A 40s warp yarn at TM 3.8. Take the same TM to a 20s and TPI falls to 17.0 — coarser yarn needs fewer turns per inch for the same twist hardness, which is precisely what the multiplier encodes.
How to use it
- Work through the input groups in order — Twist Specification. The defaults are a realistic case, so you can change one value at a time and watch what moves.
- There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
- Read Turns per Inch in the dark results panel — that is the headline figure, expressed in TPI.
- Check the supporting rows underneath (Turns per Metre, Tex Twist Factor, Surface Twist Angle and Estimated Yarn Diameter) before acting on the headline — they are where an implausible input usually shows itself first.
- Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.
Where this is used
- Ring frame and twister setting — converting the specified twist multiplier into the turns per inch the machine is geared for.
- Strength and hand trade-off — twist raises yarn tenacity up to an optimum and reduces it beyond, while raising stiffness and harshness throughout.
- Warp versus weft planning — warp needs abrasion resistance and so runs harder; weft and knitting yarn run softer for cover and handle.
- Specification translation — turning an English twist multiplier into the alpha-tex an ISO or European specification asks for.
Reading the result
Typical bands and what each one is telling you.
| Value | What it indicates |
|---|---|
| TM 2.8 to 3.4 | Knitting and soft weft. Maximum cover and softest handle, lowest yarn strength. |
| TM 3.4 to 3.8 | General weft and medium hosiery. |
| TM 3.8 to 4.5 | Warp. Enough twist to survive sizing, drawing-in and the loom. |
| TM above 5.0 | Voile and crepe. Deliberately hard, and reliant on twist setting to stay stable. |
| Twist angle above 25 degrees | Past the usual strength optimum for cotton — expect tenacity to fall and stiffness to rise. |
Assumptions and limits
- Typical multipliers: 3.0-3.6 for weft and knitting, 3.8-4.5 for warp, above 5.0 for crepe. Twist angles beyond about 25 degrees begin to cost tenacity.
- Every input is bounded to the range normal practice occupies (Twist Multiplier (TM / alpha-e) 1 to 8 TM and Yarn Count 1 to 300 Ne, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
- The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
- Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.
Standards and further reading
- ASTM D1422 — twist in single spun yarns by the untwist-retwist method.
- ASTM D1423 / ISO 2061 — twist by the direct counting method.
- ISO 17202 — determination of twist in single spun yarns, the untwist-retwist reference.
On this site
Articles that explain what this tool calculates.
Questions people ask
Why is twist quoted as a multiplier rather than as turns per inch?
Because the turns a yarn needs depend on its thickness. TM 3.8 gives 24 TPI on a 40s and 17 TPI on a 20s, and both yarns end up with roughly the same surface twist angle — the same hardness. One multiplier therefore specifies a whole count range where TPI would need a table.
How do I convert a twist multiplier into alpha-tex?
Multiply by about 957: alpha-tex is approximately 957 times the English twist multiplier. The tool does it exactly by routing through turns per metre and the square root of tex, which avoids the rounding that creeps in when the shortcut is applied twice.
Does more twist always mean a stronger yarn?
No. Tenacity rises with twist to an optimum — for cotton, commonly near TM 4.0 to 4.5 — because fibre gripping improves. Beyond that the fibres are held at too great an angle to the yarn axis and contribute less along it, so strength falls while stiffness keeps rising.