GATE Textile Engineering (XE9) Calculators
One calculator or converter per formula in the GATE XE Textile Engineering and Fibre Science syllabus, grouped by section, each with the full answer and the working.
16 calculators · 6 converters · common conversions
Yarn Manufacture
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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.
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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.
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- Spinning Production Calculator – Delivery speed and sliver hank, or spindle speed, twist and count → production in kg/h and per shift.
- Yarn Diameter Calculator – Yarn count, fibre density and packing fraction → yarn diameter, with Peirce’s cotton approximation.
Fabric Manufacture and Structure
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Fabric GSM Calculator
GSM = [EPI(1 + c₁)tex₁ + PPI(1 + c₂)tex₂] × 39.37 ÷ 1000
c crimp, tex = 590.5/Ne
Example: A 100 × 60 fabric in 30s × 30s cotton with 8 % warp and 5 % weft crimp: Fabric weight = 132.523 g/m².
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Cover Factor Calculator
Kc = K₁ + K₂ − K₁K₂/28
K = n√tex/10, n threads per cm; English K = EPI/√Ne; 28 is full cover
Example: A 100 × 60 fabric in 30s × 30s yarn: Cloth cover factor Kc = 21.41.
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- Crimp Calculator – Straightened yarn and fabric lengths → crimp and contraction; or threads per cm and crimp → Peirce h, l and θ.
- Knitted Fabric Calculator – Loop length, yarn count and Munden constants → CPC, WPC, stitch density, tightness factor and GSM.
Textile Testing
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Moisture Regain Calculator
R = (W − D)/D, M = (W − D)/W
W conditioned weight, D oven-dry weight; R = M/(1 − M)
Example: A sample weighing 110 g conditioned and 100 g oven-dry: Moisture regain R = 10 %.
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Yarn Evenness Calculator
CV = s/x̄ × 100, CVlim = 100/√n, I = CV/CVlim
n fibres in the cross-section = yarn tex ÷ fibre tex
Example: Eight cut-length masses of a 20 tex yarn spun from 1.5 dtex fibre: Coefficient of variation CV = 3.62531 %.
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- Fabric Shrinkage Calculator – Marked lengths and widths before and after washing → warp, weft and area shrinkage.
- Air Permeability Calculator – Tester flow + test area (ISO 9237, ASTM D737 presets) → permeability in mm/s, L/m²/s, cfm/ft².
- Bubble Point Pore Size Calculator – Bubble-point pressure + wetting liquid + pore shape factor → largest pore size, or the reverse.
Chemical Processing
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Beer–Lambert Calculator
A = ε l c = −log₁₀ T
ε absorptivity, l path length (cm), c concentration, T transmittance
Example: A dye solution with absorbance 0.6 in a 1 cm cell, ε = 12 000 L/(mol·cm): Concentration c = 80.3859 µmol/L.
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Kubelka–Munk Calculator
K/S = (1 − R)² ÷ 2R
R reflectance as a fraction at the wavelength of maximum absorption
Example: A dyed fabric with 20 % reflectance at λmax: K/S = 1.6.
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Dyeing Recipe Calculator
Dye (g) = weight (g) × shade %
bath (L) = weight (kg) × liquor ratio; chemical = g/L × bath
Example: 10 kg of cotton dyed at 2 % shade, 1:10 liquor, 60 g/L salt and 20 g/L soda ash: Dye required = 200 g.
Unit Converters for GATE Textile (XE9)
- Yarn Count Converter – tex, dtex, denier, Ne, Nm, worsted
- Yarn Twist Converter – TPI, TPM, turns/cm, turns/ft
- Fabric Weight (GSM) Converter – GSM, oz/yd², oz/ft², g/cm², lb/yd²
- Weight and Mass Converter – kg, g, mg, lb, oz, st, t, ton, oz t, ct
- Length Converter – m, km, cm, mm, µm, ft, in, mi, yd, nmi
- Area Converter – m², cm², mm², ft², in², test areas
Common GATE Textile (XE9) Conversions
- denier to tex
- tex to denier
- turn per inch to turn per metre
- turn per metre to turn per inch
- gram per square metre to ounce per square yard
- ounce per square yard to gram per square metre
- kilogram to pound
- pound to kilogram
- centimeter to inch
- inch to centimeter
- square meter to square foot
- square foot to square meter
How to use these GATE Textile calculators
These calculators follow the GATE XE Textile Engineering and Fibre Science syllabus: yarn manufacture, fabric manufacture and structure, textile testing and chemical processing. Counts can be entered as Ne or tex, using the exact relation tex × Ne = 590.5412.
Use them to check numerical problems such as twist multiplier, draft, production, fabric GSM, cover factor, knitted loop geometry, moisture regain, evenness and K/S. Each page states the formula and its variables, shows a worked example and gives the full unrounded answer with cut-off values for numerical answer type questions.
The yarn twist and fabric weight converters on this page handle unit changes that often appear inside these problems, such as TPI to TPM or GSM to oz/yd².