Yarn Diameter Calculator
A yarn’s diameter follows from its mass per length and how densely fibres pack: a 20s cotton yarn with φ = 0.6 is d = 0.203034 mm across.
Cotton 1.52, polyester 1.38, viscose 1.50, nylon 1.14, wool 1.31.
About 0.55–0.65 for ring-spun yarns.
0.203033527858497 mm
Full answer, then cut to fewer decimals (not rounded):
- 0.203033527858497 mm
- 0.20303352785849 mm
- 0.2030335278584 mm
- 0.203033527858 mm
- 0.20303352785 mm
- 0.2030335278 mm
- 0.203033527 mm
- 0.20303352 mm
- 0.2030335 mm
- 0.203033 mm
- 0.20303 mm
- 0.2030 mm
- 0.203 mm
- 0.20 mm
- 0.2 mm
- Yarn diameter
- 203.034 µm
- Peirce cotton estimate 1/(28√Ne)
- 0.202843 mm
- Linear density
- 29.5271 tex
- Yarn specific volume 1/(ρφ)
- 1.09649 cm³/g
Step-by-step solution
- d = √[4 × tex × 10⁻⁶ ÷ (π ρ φ)] (SI units)
- = √[4 × 29.5271 × 10⁻⁶ ÷ (π × 1520 × 0.6)] m
- = 0.203034 mm
Yarn Diameter Formula
d = √[4 × tex × 10⁻⁶ ÷ (π ρ φ)]
ρ fibre density, φ packing fraction; Peirce cotton d (in) = 1/(28√Ne)
Worked Example
A 20s cotton yarn (ρ = 1.52 g/cm³, φ = 0.6):
- d = √[4 × tex × 10⁻⁶ ÷ (π ρ φ)] (SI units)
- = √[4 × 29.5271 × 10⁻⁶ ÷ (π × 1520 × 0.6)] m
- = 0.203034 mm
Peirce cotton estimate 1/(28√Ne): 0.202843 mm · Linear density: 29.5271 tex · Yarn specific volume 1/(ρφ): 1.09649 cm³/g
More Yarn Manufacture Calculators
-
Yarn Twist Calculator
TM = TPI ÷ √Ne
αm = TPM ÷ √Nm, αtex = TPM × √tex; 1 TPI = 39.37 TPM
Example: A 20s Ne cotton yarn with 16.1 turns per inch: Twist multiplier TM = 3.6001.
-
Draft Calculator
Draft = N_out × doublings ÷ N_in
indirect counts; mechanical draft = delivery ÷ feed surface speed; actual = mechanical ÷ (1 − waste)
Example: A 0.12 hank sliver drafted to a 1 hank roving with no doubling: Actual draft = 8.33333.
-
Spinning Production Calculator
kg/h = speed (m/min) × 60 × ktex × η ÷ 1000
ring frame: delivery speed = spindle rpm ÷ TPM
Example: A card delivering 5 ktex sliver at 150 m/min and 90 % efficiency: Production = 40.5 kg/h.
Frequently asked questions
Where does Peirce’s 1/(28√Ne) come from?
It assumes cotton yarn has a specific volume of about 1.1 cm³/g; in inches d = 1/(28√Ne), or about 0.907/√Ne mm.
Why does packing fraction matter?
Yarn is part fibre and part air; a lower packing fraction (bulkier yarn) gives a larger diameter for the same count.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Yarn Diameter Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/yarn-diameter-calculator/
IEEE
Scientific Converters, "Yarn Diameter Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/yarn-diameter-calculator/