Fabric Dyeing WOF Calculator
Weigh your fibre, pick a dye class and shade, and get the exact dyestuff, salt, soda ash and water — scaled to your liquor ratio — with a live dye-bath and a water-and-energy footprint as you tune the recipe.
Fabric Dyeing WOF Calculator & Textile Coloration Guide
Textile dyeing is applied chemistry: get the ratios wrong and you waste expensive dyestuff, produce uneven or off-target shades, and pour needless salt into the waste stream. The single number that anchors every recipe is the Weight of Fibre (WOF), and once you have it, dye and auxiliaries follow as simple proportions. This calculator handles the mathematics for reactive, acid, disperse and natural dyes, and the guide below explains the chemistry behind each. Everything computes client-side and updates instantly.
The Weight of Fibre (WOF) Foundation
WOF — also called Weight of Goods (WOG) — is the dry weight of the material before scouring, and it is the universal constant that lets a recipe scale from a 50 g skein to a 500 kg roll. Every dye, mordant and most auxiliaries are dosed as a percentage of it:
Weight of chemical (dry) = WOF × (percentage required ÷ 100)
Liquor Ratio (M:L) and Water Volume
While dye quantity is bound to fibre weight, water volume is set by the Material-to-Liquor (M:L) ratio — the transport medium for the dye. Water volume equals fabric weight (kg) × the ratio, so 1 kg at 1:20 needs 20 litres. Low ratios (1:3 to 1:6) suit modern airflow machines and save water, energy and chemicals; high ratios (1:20 to 1:40) suit artisanal immersion and keep the cloth relaxed and even. Critically, salt and alkali in reactive dyeing are dosed in grams per litre of the bath, not as a WOF percentage — so their absolute mass depends on the liquor volume you choose here.
| Context | Typical M:L | Water per 1 kg | Character |
|---|---|---|---|
| Advanced industrial (airflow) | 1:3 – 1:6 | 3–6 L | Highly efficient, needs strong circulation |
| Standard industrial | 1:8 – 1:15 | 8–15 L | Balanced for general woven and knit |
| Artisanal immersion (bucket) | 1:20 – 1:40 | 20–40 L | High water use, very even shades |
Reactive Dyes (Procion MX) for Cellulose
Reactive dyes bond covalently with cellulose (cotton, linen, hemp, viscose) in cold water, and need two auxiliaries: a large dose of non-iodised salt to drive the dye onto the fibre (exhaustion), and an alkali — soda ash — to raise pH and trigger fixation. Both are dosed per litre of bath and rise with shade depth. Deep blacks need roughly double the salt of a pale shade, because aggressive exhaustion is the only way to force that much dye into the fibre rather than down the drain.
| Shade depth | Dye (WOF) | Salt (g/L) | Soda ash (g/L) |
|---|---|---|---|
| Very pale | 0.2–0.5% | 20–35 | 5.0–5.5 |
| Medium | 1.0–2.0% | 35–40 | 5.5–10.0 |
| Heavy / dark | 3.0–4.0% | 45–60 | 5.5–20.0 |
| Deepest black | 6.0% | 67.5 | 7.5 |
The correct sequence matters: dissolve salt and dye first and agitate 10–15 minutes for exhaustion, then add the dissolved soda ash in intervals so fixation is level rather than blotchy. The calculator prints this sequence with your exact quantities.
Acid Dyes for Protein and Nylon
Acid dyes are anionic and colour wool, silk and nylon by forming ionic bonds under acidic conditions. The right pH depends on molecule size: leveling dyes are small, weak-affinity, and need a strong acid to reach pH 2.0–3.0; milling dyes are medium-to-large with better wet-fastness at pH 4.0–6.0 using a weak acid like acetic; metal-complex (1:2) dyes are large, contain chromium or cobalt, give the best light-fastness and work near neutral (pH 6.0–7.0). Leveling agents (about 1 g/L) and ammonium sulphate (about 2 g/L) slow the strike rate to prevent streaky "barré" defects.
Disperse Dyes for Polyester
Polyester is dyed with non-ionic disperse dyes that are near-insoluble in water and hire dispersing agents to stay suspended until, at about 130 °C under pressure (HTHP), the polymer relaxes and lets the dye diffuse in. If you only have atmospheric equipment capped at 100 °C, a chemical carrier is required — it swells the fibre at lower temperature so the dye can enter. The calculator adds the carrier automatically when you flag atmospheric equipment.
Natural Dyes and Mordant Chemistry
Most natural dyes are not substantive; they need a mordant — a metal-salt bridge — to bind colour to fibre. Mordants are dosed on dry WOF: alum (the universal standard) at 15%, aluminium acetate for cellulose at 5–8%, aluminium triformate (a cold-water option) at 5–8%, and iron as a post-mordant colour-shifter at just 2% — more than that weakens the fibre. Tannins help cellulose accept alum and can themselves tint the final hue. Tinctorial strength varies enormously: a medium red from madder root needs a huge 50% WOF, while a deep crimson from cochineal needs only 5%.
Computer Colour Matching: Kubelka-Munk
Industrial colour matching replaced the eye with optics decades ago. The single-constant Kubelka-Munk model maps a measured decimal reflectance R to the ratio of a colorant's absorption (K) and scattering (S):
K/S = (1 − R)² ÷ (2R)
Its power is linearity: because K/S adds linearly with concentration, a match engine can solve the concentrations of several mixed dyes that reproduce a target reflectance, as (K/S)mix = (K/S)substrate + c₁(K/S)dye1 + c₂(K/S)dye2 + …. The model assumes an ideal turbid layer and breaks down for blended pre-dyed fibres, where a Saunderson correction for surface reflections restores accuracy.
Perceptual Colour Difference: CIEDE2000
To judge how close a dyed sample is to the standard, modern labs use ΔE₀₀ (CIEDE2000) rather than a plain Euclidean distance in LAB space, because the eye is non-uniformly sensitive across hue, chroma and lightness. CIEDE2000 weights each axis with scaling factors SL, SC, SH and adds a rotational term RT to correct the troublesome blue region — aligning the mathematics with human perception. The cutting edge goes further still, using neural networks trained with CIEDE2000 as a loss function to reverse-engineer viable recipes from a target colour.
Eco-Metrics: Why Liquor Ratio Is a Sustainability Lever
Dyeing is among the most resource-intensive stages in textiles, and the M:L ratio is the biggest lever a dyer controls. Moving from 1:15 to 1:6 cuts water roughly 30–50%, and because there is less water to heat, it saves 20–35% of the thermal energy to reach temperature. Concentrated baths also exhaust dye more completely, so less salt is needed and the dissolved-solids (TDS) load on effluent treatment falls. The calculator's eco-panel estimates the water and energy saved against a traditional 1:20 bath so the trade-off is visible as you adjust the recipe.
Frequently Asked Questions
What is the formula for Weight of Fibre (WOF)?
WOF is the dry weight of the fabric before scouring, and every dye and auxiliary is dosed as a percentage of it: Weight of chemical = WOF × (percentage ÷ 100). A 450 g batch at 50% madder needs 225 g of dye. It scales to any batch size because it's proportional to fibre weight.
How much salt do I need for Procion reactive dye?
Salt is dosed per litre of bath and rises with depth: pale 20–35 g/L, medium 35–40, heavy/dark 45–60, deepest black ~67.5 g/L. Multiply by your total liquor volume. Deep shades need roughly double the salt of pale ones to force exhaustion.
What liquor ratio should I use?
M:L is fabric weight to water volume. Airflow machines 1:3–1:6, standard industrial 1:8–1:15, bucket immersion 1:20–1:40. Lower saves water, energy and improves exhaustion; higher keeps cloth even. 1 kg at 1:20 = 20 L.
What percentage of alum mordant do I use?
Alum is 15% WOF for both protein and cellulose. Aluminium acetate (cellulose) is 5–8%, aluminium triformate 5–8%, and iron as a post-mordant just 2% WOF — more weakens the fibre. All are on dry fibre weight.
How do I convert a dye % into a stock solution volume?
Required solution volume (ml) = (fabric g × shade %) ÷ stock concentration %. For 450 g at 2% shade from a 5% stock: 450 × 2 ÷ 5 = 180 ml. Switch the calculator to stock mode to dose liquids directly.
Does a lower liquor ratio really save water and energy?
Yes. 1:15 → 1:6 cuts water ~30–50% and thermal energy ~20–35%, since there's less to heat. Concentrated baths also exhaust dye better, so less salt and a lower TDS load on effluent treatment. The eco-panel estimates the savings.
Scope and disclaimer. This tool provides dyeing-recipe planning estimates from standard WOF, liquor-ratio and auxiliary-concentration conventions, for informational and educational use. Dyes and auxiliaries vary by manufacturer, and some acids and mordants are hazardous — always follow the supplier's safety data sheet, wear appropriate protection, and test on a sample. It is not professional or safety advice.