Calculating NCO:OH Ratio and Hardener Demand
The three-step arithmetic derived from first principles, a full worked example, and why a waterborne system needs more isocyanate than the stoichiometry alone suggests.
💡 The one-paragraph version
Count the moles of hydroxyl in your resin charge. Multiply by the NCO:OH index you have chosen. Convert the resulting moles of isocyanate into a weight of hardener using the hardener's NCO content. That is the whole calculation - three steps and two constants. Everything difficult about it lies in making sure the numbers you feed in mean what you think they mean.
📦 Why There Is No Fixed Mix Ratio
Formulators arriving from ready-mixed two-pack products often expect a mix ratio to be a property of the system - 4:1, 5:1, printed on the tin. For a finished coating sold as a matched pair, it is. For raw materials it is not, because the ratio is a consequence of two independent numbers that you are free to change.
Change the resin grade and the hydroxyl content changes, so the ratio changes. Change hardener supplier and the NCO content changes, so the ratio changes again. Decide to run a higher index for better cure in a humid workshop, and it changes a third time. A mix ratio quoted without stating which resin, which hardener and which index it belongs to is not information - it is a coincidence.
The good news is that the calculation is short, and once you have set it up as a spreadsheet you can re-run it in seconds every time one of the inputs moves.
🧮 The Three-Step Calculation
Step 1 - Hydroxyl equivalents in the resin charge
An equivalent, here, is one mole of reactive group. You want the number of moles of hydroxyl your resin charge contains. Only the solid resin carries hydroxyl, so the water fraction has to come out first.
📐 Step 1
OH equivalents = (resin weight × solids fraction × OH% ÷ 100) ÷ 17.008
The constant 17.008 is the molar mass of the hydroxyl group in g/mol. Dividing a mass of hydroxyl by it gives moles. If your supplier states a hydroxyl number in mg KOH/g rather than a percentage, divide it by 33 first to get OH%, or divide 56 106 by the hydroxyl number to get the equivalent weight directly - the conversions are covered in our guide to hydroxyl content and crosslink density.
⚠️ The solids fraction is only correct if your OH% is stated on solid resin. If your supplier quotes hydroxyl on the dispersion as supplied, omit the solids fraction - multiplying by it a second time will halve your answer. At 45% solids the two conventions differ by a factor of about 2.2. Confirm the basis in writing before you run this step.
Step 2 - Isocyanate equivalents you need
📐 Step 2
NCO equivalents = OH equivalents × NCO:OH index
At an index of 1.0:1 you are supplying exactly one isocyanate group per hydroxyl group - perfect stoichiometry, no excess. For solvent-borne systems that is roughly where you would sit, perhaps a little above. For waterborne systems it is not enough, for reasons covered further down.
Step 3 - Convert to a hardener weight
📐 Step 3
Hardener weight = NCO equivalents × (4 202 ÷ hardener NCO%)
The bracketed term is the hardener's NCO equivalent weight in g/eq.
The constant 4 202 is not arbitrary. The isocyanate group –NCO has a molar mass of 42.02 g/mol. A hardener at, say, 20% NCO contains 42.02 g of isocyanate group in every 210.1 g of product, so its equivalent weight is 42.02 ÷ 0.20 = 210.1 g/eq. Expressing the NCO content as a percentage rather than a fraction folds a factor of 100 into the numerator, which is where 42.02 × 100 = 4 202 comes from.
✅ Worth internalising: hardener equivalent weight = 4 202 ÷ NCO%. It is the single most useful derived number in 2K formulation, and it lets you compare two hardeners on a like-for-like basis instead of on price per kilo.
🔢 A Complete Worked Example
Take a batch of 500 g of a waterborne acrylic polyol at 42% solids with a hydroxyl content of 2.2% on solid resin, to be cured with an aliphatic polyisocyanate at 20% NCO, run at an index of 1.5:1.
Step 1 - hydroxyl equivalents
Solids present = 500 × 0.42 = 210 g
Hydroxyl mass = 210 × 0.022 = 4.62 g
OH equivalents = 4.62 ÷ 17.008 = 0.2716 eq
Step 2 - isocyanate equivalents at 1.5:1
NCO equivalents = 0.2716 × 1.5 = 0.4074 eq
Step 3 - hardener weight
Hardener eq weight = 4 202 ÷ 20 = 210.1 g/eq
Hardener weight = 0.4074 × 210.1 = 85.6 g
✅ Result: 500 g of resin takes 85.6 g of hardener - a mix ratio of roughly 5.8 : 1 by weight.
Notice what the answer is not. It is not a round number, it is not the same as your last resin, and it does not correspond to any ratio you could have guessed. Notice also that it is a weight ratio. If your shop mixes by volume you must convert using the densities of both components, and the conversion is not optional - resin and hardener densities differ enough that treating a weight ratio as a volume ratio introduces a substantial error.
📊 How Sensitive Is the Answer?
Holding the same 500 g resin charge, here is how the hardener weight responds to the index you choose:
| NCO:OH index | Hardener at 20% NCO | Mix ratio by weight | Practical read |
|---|---|---|---|
| 1.0 : 1 | 57.1 g | 8.8 : 1 | Stoichiometric; under-cures in a waterborne system |
| 1.2 : 1 | 68.5 g | 7.3 : 1 | Lower end of the usual waterborne window |
| 1.5 : 1 | 85.6 g | 5.8 : 1 | A common starting point |
| 1.8 : 1 | 102.7 g | 4.9 : 1 | Humid conditions or high water sensitivity |
| 2.0 : 1 | 114.1 g | 4.4 : 1 | Upper end; watch film build and CO₂ |
And here is how it responds to the hardener's NCO content, holding the index at 1.5:1:
| Hardener NCO% | Equivalent weight (g/eq) | Hardener required |
|---|---|---|
| 12% | 350.2 | 142.7 g |
| 15% | 280.1 | 114.1 g |
| 17% | 247.2 | 100.7 g |
| 20% | 210.1 | 85.6 g |
| 23% | 182.7 | 74.4 g |
💡 This is why hardener price per kilogram is a poor comparison. A hardener at 23% NCO delivers the same crosslinking as one at 12% NCO using roughly half the weight. Compare cost per equivalent, not cost per kilo - multiply the price per kilo by the equivalent weight and you have a number that means something.
For the three hydroxyl grades in our own range (1.0, 2.4 and 3.3 wt% on solids at 45% solids), the equivalent figures at both 1.0:1 and 1.5:1 are tabulated on the three hydroxyl grades with worked hardener figures so you can check your own spreadsheet against them.
💧 Why the Index Runs Above 1:1 - and What It Costs
In a solvent-borne system, isocyanate has essentially one thing to react with: your hydroxyls. In a waterborne system it has a large excess of a competing reactant present from the first moment of mixing.
The competing reaction runs in two stages. Isocyanate reacts with water to form an unstable carbamic acid, which immediately decomposes into a primary amine and carbon dioxide. That amine is far more nucleophilic than any hydroxyl, so it reacts almost instantly with a second isocyanate group to form a urea. Net result: two isocyanate groups consumed, one urea linkage formed, one molecule of carbon dioxide released - and none of it doing the crosslinking you intended.
⚗️ The competing reaction
R–NCO + H₂O → [R–NH–COOH] → R–NH₂ + CO₂↑
R–NH₂ + R'–NCO → R–NH–CO–NH–R' (urea)
Because the loss is unavoidable, formulators supply an excess - commonly between 1.2:1 and 2:1 - so that enough isocyanate survives to reach the hydroxyls. Exactly where in that band you should sit depends on your resin's water content, your ambient humidity, your film build and how long the mixture stands before application. It is an empirical number: establish it on your own panels rather than adopting someone else's.
The excess is not free, and the costs are worth naming:
- 💰 Cost. The hardener is typically the most expensive component in the mixed system. Moving from 1.2:1 to 2:1 raises the hardener bill by about two thirds.
- 🫧 Carbon dioxide. Every mole of isocyanate lost to water releases a mole of gas that must leave before the film closes. In thin coats it escapes harmlessly. In thick films it is trapped and you get bubbles, pinholes and a hazy surface.
- 🧱 Urea content. Urea linkages are harder and more polar than urethane linkages. A significant urea fraction changes the film you designed - usually toward greater hardness and reduced flexibility.
- ⏱️ Nothing gained on pot life. A higher index does not extend your working window; the water reaction proceeds regardless.
💡 If you are seeing pinholing, reduce film build per coat before you change anything else. Two thinner coats will very often solve a defect that no amount of formulation adjustment fixes, because the problem is gas transport rather than chemistry. The full diagnostic sequence is in our troubleshooting guide for 2K waterborne coatings.
⚠️ Five Ways a Correct Formula Gives a Wrong Answer
The arithmetic is not where people go wrong. The inputs are.
1️⃣ The hydroxyl basis
On solids or as supplied. This single ambiguity accounts for more failed 2K waterborne panels than any other cause. Confirm it in writing, on the technical data sheet, every time you change grade or supplier.
2️⃣ The hardener's NCO basis
NCO content is normally stated on the product as supplied, which matters because many hardeners are shipped in solvent at 70–90% solids. If a data sheet quotes NCO on solid resin, you must correct for the solvent - otherwise you will undercharge by the solvent fraction. The mirror image of the hydroxyl trap, and equally easy to miss.
3️⃣ Weight versus volume
The calculation returns a weight. Converting to volume requires the density of each component at working temperature. Shops that mix by volume from a weight-derived ratio, without converting, are running a systematic error on every batch.
4️⃣ Other active hydrogen in the formulation
Isocyanate reacts with anything carrying an active hydrogen, not only your resin's hydroxyls. Glycol ether coalescents with a free hydroxyl group, alcohol co-solvents, some wetting agents and dispersants, and residual moisture in pigment pastes and fillers all consume isocyanate. Coalescents in particular are usually present at a few percent - enough to matter. If your formulation is additive-heavy, expect the empirically optimal index to sit higher than the arithmetic alone predicts. ⚗️ Where you have a choice, a coalescent without a free hydroxyl avoids the problem entirely.
5️⃣ Calculating on the resin rather than the finished paint
If your resin is one component of a pigmented formulation, Step 1 must use the mass of resin in the batch, not the mass of the batch. Sounds obvious; it is a routine slip when a formulation sheet lists a let-down stage and the resin arrives in two separate additions.
🧪 Verifying the NCO Content You Were Given
NCO content is determined by a straightforward back-titration: the sample is reacted with an excess of di-n-butylamine, and the unconsumed amine is titrated with acid. The established methods are ASTM D2572, published by ASTM International, and ISO 14896, available through the ISO Online Browsing Platform. Both are within the reach of a normal coatings QC laboratory.
It is worth checking on receipt for one specific reason: NCO content falls during storage if a container has been opened and exposed to humid air, because atmospheric moisture consumes isocyanate exactly as formulation water does. A part-used drum that has stood through a humid summer may titrate meaningfully below its nominal figure - and your calculation will be silently wrong from that point on. Keep hardener containers sealed, blanket with dry nitrogen where practical, and re-check NCO on anything that has been open for an extended period.
🚨 Handling polyisocyanates safely
Isocyanates are respiratory sensitisers and a leading cause of occupational asthma. Sensitisation is generally permanent - once a worker reacts, further exposure at any level can trigger an attack. Spray application produces the highest-risk exposures and requires appropriate respiratory protection, ventilation and training. See OSHA's guidance on isocyanates, and note that industrial and professional users in the EU are subject to a mandatory training requirement under the ECHA diisocyanate restriction. A waterborne resin lowers solvent exposure; it does not lower isocyanate exposure at all.
📋 A Working Protocol
- ✅ Build it once as a spreadsheet, with resin weight, solids, OH%, OH basis, hardener NCO%, NCO basis and index as named input cells. Re-running takes seconds; re-deriving by hand invites arithmetic slips.
- ✅ Bracket the index rather than guessing it. Prepare panels at 1.2, 1.5 and 1.8 and test properties after a full cure, not at 24 hours. Waterborne systems continue to develop, and an early test will condemn a film that would have passed a week later.
- ✅ Re-optimise the index when conditions change - a different season, a different workshop, a higher film build or a reformulated additive package all move the answer.
- ✅ Mix only what you will use inside the pot life, and discard the remainder rather than stretching it to the end of a shift. Because a waterborne 2K mixture gives no viscosity warning as it expires, this is a discipline rather than a judgement call - see our article on pot life in 2K waterborne systems.
- ✅ Record the index alongside every test result. A panel result without its index is not reproducible information.
❓ Frequently Asked Questions
Q1. What index should I start with?
1.5:1 is a reasonable first attempt for a general-purpose waterborne acrylic polyol, but treat it as the middle of a bracket rather than an answer. Prepare panels at 1.2, 1.5 and 1.8 under your own conditions and let the results decide. A humid workshop, a water-sensitive formulation or a high film build all push the optimum upward; a tightly controlled line at moderate humidity may sit comfortably lower and save you real money on hardener.
Q2. Can I just run a very high index to be safe?
No - it is not a safety margin, it is a different failure mode. Surplus isocyanate does not sit inert; it reacts with water, generating more carbon dioxide that has to escape before the film closes, and more urea than you designed for. You get bubbles and pinholing at normal film builds, a harder and less flexible film, and a hardener bill you did not need to pay. Over-indexing produces defects just as reliably as under-indexing does.
Q3. Does the index need changing when I change hydroxyl grade?
The index is a ratio, so in principle it carries across - the calculation already scales the hardener weight with the hydroxyl content. In practice a higher hydroxyl grade at the same index means substantially more hardener in the mix, which means more isocyanate available to meet water and more carbon dioxide generated. If you move up a grade and start seeing pinholing at a film build that was previously fine, that is the mechanism, and reducing film build or trimming the index is the response.
Q4. How do I compare two hardeners on cost?
Multiply the price per kilogram by the equivalent weight (4 202 ÷ NCO%) to get a cost per equivalent. That figure is directly comparable; price per kilogram is not, because a high-NCO hardener delivers more crosslinking per kilo. A hardener that looks 20% more expensive per kilo can easily be cheaper per equivalent. Do also weigh the non-price differences - conventional and water-dispersible types behave quite differently on the shop floor, which we cover in our hardener comparison guide.
Q5. My mixed coating is fine but the film stays soft. Is my ratio wrong?
Possibly, but check three cheaper explanations first. Had the pot life expired before application? A waterborne 2K mixture sprays perfectly well after the usable isocyanate has gone. Was a conventional polyisocyanate properly emulsified? Poorly dispersed hardener sits as droplets instead of forming crosslinks. And was the panel tested after a full cure? Waterborne systems need time and temperature, and premature testing fails films that would have passed. Only after those three does a ratio error become the likely answer.
Q6. Do you supply the hardener as well?
Not currently - we supply the polyol side, and it is better to say so plainly than to let you discover it at order stage. We will tell you the NCO content and hardener type each grade is designed around so that you can source it correctly, and everything in this article lets you size the charge against whatever hardener you buy.
📚 Continue Reading
Hydroxyl Content and Crosslink Density
Where Step 1's OH% comes from, how to convert it, and the on-solids basis trap that breaks this calculation.
Read the guide →Conventional vs Water-Dispersible Polyisocyanate
Which hardener you calculate against, and why the right answer depends on your shop floor more than your chemistry.
Read the guide →Pot Life in 2K Waterborne Polyurethane
Why a correctly calculated mixture still fails if it stands too long - and why viscosity will not warn you.
Read the guide →Also see: What Is Waterborne Hydroxyl Acrylic Resin? · Waterborne Hydroxyl Acrylic Resin (2K Polyol) · All Coatings & Inks Chemicals
📩 Check Your Calculation Against Our Figures
Send us the substrate, the service condition the finished surface has to survive, your application method and your intended film build, and we will recommend one or two hydroxyl grades along with the hardener NCO content each is designed around. Data sheets state the hydroxyl basis explicitly rather than leaving you to assume it, and come with SDS, co-solvent content, VOC figures for your market and laboratory samples. We reply within 24 hours.
🔗 View the full Waterborne Hydroxyl Acrylic Resin product page →
Xiamen Sinolook Oil Co., Ltd. - Waterborne Hydroxyl Acrylic Resin (WAR). Hydroxyl content is stated on solid resin. The resin and hardener figures used in the worked example and sensitivity tables are illustrative values chosen to demonstrate the arithmetic and are not the specification of any particular grade or hardener. Verify all inputs against the technical data sheet and certificate of analysis for the materials you are actually using, and establish your own NCO:OH index empirically under your own application conditions. Polyisocyanate hardeners are respiratory sensitisers - follow the hardener manufacturer's safety data sheet and applicable national regulations. Do not allow waterborne dispersions to freeze.
