Yarn Spinning Formulas: Count, Draft, Twist and Production

The core yarn spinning formulas are count conversion (tex = 590.5 ÷ Ne = 1000 ÷ Nm = denier ÷ 9), draft (draft = feed linear density ÷ delivered linear density, or delivery roller surface speed ÷ feed roller surface speed), twist (TPI = twist multiplier × √Ne, and TPI = spindle rpm ÷ front roller delivery in inches per minute) and production (kg per hour = delivery speed in m/min × sliver or yarn linear density in g/m × 60 × efficiency ÷ 1000). On a ring frame, output per spindle in an 8-hour shift is 0.0072 × spindle rpm × efficiency ÷ (TPI × Ne) kg. This page gives every formula in one table, then works each one through with real numbers for the card, drawframe, ring frame and winder, explains where the constants come from, and links each formula to the site’s calculator for it.

Last verified: 8 October 2026. Efficiency is written as a fraction in every formula (90% = 0.90). Sources are listed at the end.

Spinning formulas at a glance

What you want	Formula	Where it is explained
Convert a yarn count	tex = 590.5 ÷ Ne = 1000 ÷ Nm = denier ÷ 9 = dtex ÷ 10	Yarn count
Grams per metre of a sliver, roving or yarn	g/m = 0.5905 ÷ Ne = tex ÷ 1000 (1 ktex = 1 g/m)	Yarn count
Draft from linear density	draft = feed linear density ÷ delivered linear density (same units)	Draft
Draft from roller speeds	draft = delivery roller surface speed ÷ feed roller surface speed	Draft
Draft over several zones	total draft = break draft × main draft	Draft
Hank after doubling and drafting	hank delivered = hank fed × draft ÷ doublings	Draft
Actual and mechanical draft	actual draft = mechanical draft × 100 ÷ (100 − waste %)	Draft
Twist from the twist multiplier	TPI = TM × √Ne; TPM = TPI × 39.37	Twist
Twist from the machine	TPI = spindle rpm ÷ front roller delivery (inches per minute)	Twist
Front roller delivery	inches per minute = π × front roller diameter (inches) × front roller rpm	Twist
Production of a card, drawframe or winder	kg/h = delivery speed (m/min) × ktex × 60 × efficiency ÷ 1000	Production
The same in English count	kg per 8 h = 0.2835 × delivery speed (m/min) × efficiency ÷ Ne, per delivery	Production
Ring frame output per spindle	kg per 8 h = 0.0072 × spindle rpm × efficiency ÷ (TPI × Ne)	Ring frame
Hanks per spindle	hanks per 8 h = spindle rpm × efficiency ÷ (63 × TPI)	Ring frame
Ring traveller speed	m/s = π × ring diameter (mm) × spindle rpm ÷ 60,000	Ring frame

Yarn count and linear density

A count states how heavy a length of yarn is. Indirect systems give length per unit mass, so a bigger number is a finer yarn: the English cotton count Ne is the number of 840-yard hanks in one pound, and the metric count Nm is the number of kilometres in one kilogram. Direct systems give mass per unit length, so a bigger number is a coarser yarn: tex is grams per 1000 metres (the international system set out in ISO 1144), decitex is grams per 10,000 metres and denier is grams per 9000 metres.

Where 590.5 comes from. The yard is exactly 0.9144 m and the pound exactly 453.59237 g. One Ne is 840 yards (768.1 m) per pound, so it weighs 453.59237 ÷ 768.096 = 0.5905 g per metre, or 590.5 g per 1000 m. That gives tex × Ne = 590.5, grams per metre = 0.5905 ÷ Ne, and Nm = 1.693 × Ne. Published conversion factors for every system are tabulated in ASTM D2260; the count itself is measured by weighing skeins of known length (ISO 2060, ASTM D1907).

Worked example: a 30s Ne cotton yarn	Working	Result
Tex	590.5 ÷ 30	19.68 tex
Metric count	1000 ÷ 19.68	Nm 50.8
Denier	19.68 × 9	177.2 den
Decitex	19.68 × 10	196.8 dtex
Grams per metre	0.5905 ÷ 30	0.01968 g/m

The same arithmetic runs in the yarn count converter, set to 30s Ne, which also gives worsted and jute counts. For cotton fibre, micronaire is read in micrograms per inch, so micronaire ÷ 25.4 gives micrograms per millimetre, which is the same thing as tex: a micronaire of 4.0 is about 0.157 tex (157 millitex). Micronaire is an airflow reading that also responds to fibre maturity, so treat that figure as an estimate of fineness.

Draft

Draft is how many times a strand is drawn out. The rollers that deliver the strand turn faster than the rollers that feed it, so the strand leaves longer and thinner by the ratio of their surface speeds. Because mass flowing in equals mass flowing out, the same ratio appears in the linear densities: draft = feed linear density ÷ delivered linear density = delivery surface speed ÷ feed surface speed. Use the same unit on both sides (ktex with ktex, or hank with hank, remembering that hank rises as the strand gets finer, so draft = hank delivered ÷ hank fed).

• Zones multiply. In a three-roller drafting zone the break draft is middle roller surface speed ÷ back roller surface speed, the main draft is front roller surface speed ÷ middle roller surface speed, and total draft = break draft × main draft.
• Doubling cancels draft. Feeding several ends together multiplies the feed linear density, so hank delivered = hank fed × draft ÷ doublings.
• Waste makes actual draft higher than mechanical draft. The gearing sets the mechanical draft. If a machine removes waste, less mass leaves than entered, so the delivered strand is finer than the gearing alone predicts: actual draft = mechanical draft × 100 ÷ (100 − waste %).

Worked example	Working	Draft
Card: chute feed 500 g/m, sliver 5 g/m (5 ktex)	500 ÷ 5	100 actual; with 5% waste removed the mechanical draft is 100 × 0.95 = 95
Drawframe: 8 ends of 5 ktex sliver in, 5 ktex out	(8 × 5) ÷ 5	8, equal to the doublings, so the hank is unchanged
Ring frame: roving 1.0 hank to 30s Ne yarn	30 ÷ 1.0	30

Calculators: card sliver draft, drawframe draft and doubling, roving hank to yarn count draft and draft constant.

Twist

Twist is what holds staple fibres together as yarn. A finer yarn has fewer fibres in its cross-section and needs more turns per inch to reach the same twist angle, which is why twist is set through a twist multiplier (TM, also written αe) rather than directly: TPI = TM × √Ne, and turns per metre TPM = TPI × 39.37. In the tex system the twist factor is α tex = TPM × √tex, and the two multipliers are related by α tex ≈ 957 × TM. Twist is measured by untwisting a specimen of known length (ISO 2061), and its direction is stated as S or Z.

On the machine, every turn of the spindle puts one turn into the yarn delivered in that time, so TPI = spindle rpm ÷ front roller delivery in inches per minute, where delivery = π × front roller diameter (inches) × front roller rpm.

Worked example	Working	Result
30s Ne at twist multiplier 4.0	4.0 × √30 = 4.0 × 5.477	21.91 TPI = 862.6 TPM; α tex = 862.6 × √19.68 = 3,827
Front roller 1 inch diameter at 200 rpm	π × 1 × 200	628.3 inches per minute
Spindle at 17,000 rpm with that delivery	17,000 ÷ 628.3	27.06 TPI

Calculators: twist multiplier to TPI and TPM, roving twist and flyer speed and resultant count of plied yarns.

Production: card, drawframe and winder

Every machine that delivers a sliver or a yarn at a known speed follows one formula. Delivery speed in metres per minute times linear density in grams per metre is grams per minute; times 60 is grams per hour; divided by 1000 is kilograms per hour; times efficiency is what the machine actually makes. Because 1 ktex is exactly 1 g/m, kg/h = delivery speed (m/min) × ktex × 60 × efficiency ÷ 1000. For a yarn quoted in tex, divide by a further 1000.

The 0.2835 constant. Older books write the same formula in English count: kg per 8 hours = 0.2835 × delivery speed (m/min) × efficiency ÷ Ne, per delivery. The constant is 480 minutes × 1.0936 yards per metre ÷ 840 yards per hank ÷ 2.2046 pounds per kilogram = 0.2835. It is often printed as 0.2836, a rounding difference of 0.04%.

Worked example	Working	Result
Card at 150 m/min, 5 ktex sliver, 90% efficiency	150 × 5 × 60 × 0.90 ÷ 1000	40.5 kg/h; 324 kg per 8 hours
The same card in English count (5 ktex = 0.1181 Ne)	0.2835 × 150 × 0.90 ÷ 0.1181	324 kg per 8 hours, the same answer
Drawframe at 500 m/min, 5 ktex, 80% efficiency	500 × 5 × 60 × 0.80 ÷ 1000	120 kg/h per delivery; 240 kg/h on a two-delivery frame
Winding drum at 1,200 m/min, 30s Ne (19.68 tex), 80% efficiency	1,200 × 19.68 × 60 × 0.80 ÷ 1,000,000	1.13 kg/h per drum

Calculators: card production rate and total draft and drawframe output.

Ring frame production

A ring frame delivers yarn only as fast as the twist allows: the front roller feeds spindle rpm ÷ TPI inches of yarn per minute. Converting that length to mass through the count gives pounds per spindle per hour = 60 × spindle rpm ÷ (36 × 840 × TPI × Ne), where 36 turns inches into yards and 840 yards make a hank. Over an 8-hour shift and in kilograms this becomes kg per spindle = 0.0072 × spindle rpm × efficiency ÷ (TPI × Ne). In hanks it is spindle rpm × efficiency ÷ (63 × TPI), since 36 × 840 ÷ 480 minutes = 63. Traveller speed in metres per second is π × ring diameter (mm) × spindle rpm ÷ 60,000; the traveller runs slightly slower than the spindle, so this is its upper figure.

Worked example: 40s Ne at 17,000 rpm	Working	Result
Twist at TM 3.8	3.8 × √40	24.03 TPI
Front roller delivery	17,000 ÷ 24.03 × 0.0254	17.97 m/min
Output per spindle, 95% efficiency, 8 hours	0.0072 × 17,000 × 0.95 ÷ (24.03 × 40)	0.121 kg (15.1 g per spindle hour)
Hanks per spindle, 8 hours	17,000 × 0.95 ÷ (63 × 24.03)	10.67 hanks
Frame of 1,200 spindles	0.121 × 1,200	145 kg per shift (18.1 kg/h)
Traveller speed on a 42 mm ring	π × 42 × 17,000 ÷ 60,000	37.4 m/s

Calculators: ring frame production, set to this example and traveller speed and ring diameter limit.

Questions

What is the formula for draft in spinning?

Draft = feed linear density ÷ delivered linear density, which equals delivery roller surface speed ÷ feed roller surface speed. In hanks it is hank delivered ÷ hank fed, multiplied by the number of doublings when several ends are fed together.

What is 0.2835 (or 0.2836) in spinning production formulas?

It converts metres per minute into kilograms per 8-hour shift for a strand counted in Ne: 480 minutes × 1.0936 yards per metre ÷ 840 yards per hank ÷ 2.2046 pounds per kilogram = 0.2835. Production in kg per 8 hours = 0.2835 × delivery speed × efficiency ÷ Ne.

How do you calculate TPI from the twist multiplier?

Multiply the twist multiplier by the square root of the English count: TPI = TM × √Ne. A 30s yarn at TM 4.0 needs 4.0 × 5.477 = 21.9 turns per inch, or 862.6 turns per metre.

How do you calculate ring frame production?

Output per spindle in an 8-hour shift is 0.0072 × spindle rpm × efficiency ÷ (TPI × Ne) kg. Multiply by the number of spindles for the frame. At 17,000 rpm, 24.03 TPI, 40s and 95% efficiency that is 0.121 kg per spindle and 145 kg for a 1,200-spindle frame.

How do you convert Ne to tex?

Divide 590.5 by the Ne count: tex = 590.5 ÷ Ne. A 30s yarn is 19.68 tex and a 40s yarn is 14.76 tex. The conversion works both ways, so Ne = 590.5 ÷ tex.

What is the difference between actual draft and mechanical draft?

Mechanical draft is set by the roller speeds. Actual draft is measured from the strand going in and coming out. They differ when the machine removes waste, as a card or comber does: actual draft = mechanical draft × 100 ÷ (100 − waste %).

Sources and corrections

• Exact yard and pound, from which 590.5, 0.5905, 0.2835 and 0.0072 are derived: NIST, Special Publication 811, Guide for the Use of the International System of Units.
• Count systems, measurement and twist: the site’s records for ISO 1144 (tex system), ASTM D2260 (conversion tables), ISO 2060 and ASTM D1907 (linear density by the skein method) and ISO 2061 (twist).
• Draft, twist and production relations: W. Klein, The Technology of Short-staple Spinning and A Practical Guide to Ring Spinning (Manual of Textile Technology, The Textile Institute); P. R. Lord, Handbook of Yarn Production (Woodhead Publishing).

Change log. 8 October 2026: rewritten as a worked guide, with every formula in one table and a worked example for each machine. Corrected from the earlier version of this page: its card and winding production formulas in kg per hour carried an extra factor of 36 (inches per yard) although the speed was already in metres, which understated output 36 times (a card at 150 m/min making 40.5 kg/h came out at 1.13 kg/h); the row for hanks delivered ran two formulas together; the hanks-per-shift constant is 63, not 62.89; the 8-hour production constant is 0.2835 (0.2836 is a rounding); and denier to tex is ÷ 9 (× 0.111), not × 0.11. The worked examples use the site’s calculators as they stood on this date.

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