> ## Documentation Index > Fetch the complete documentation index at: https://docs.plastics.com/llms.txt > Use this file to discover all available pages before exploring further. # Formulation calculators and formulas > Explore 22 blend-property calculators and five batch and conversion tools, including their equations, inputs, units, and limitations. The formulation tools help you scale a recipe, convert measured quantities, and estimate properties of a blend. This reference explains the calculations behind the current catalog: **22 property calculators and five batch and conversion tools**. Open **Formulations → Property calculators** to browse the overview, search by property, method, or ingredient input, and filter by calculation type. Use **Open Reformulation Studio** to work with a formula. The overview also links from the **Formulation calculators** setting in ChatBot setup. ## Choose a calculation | Group | Calculators | What they do | | - | - | - | | Batch and conversions | Batch scaling, active-content balance, mass conversion, mass/volume conversion, viscosity conversion | Calculate quantities from values you supply. | | Mixing rules | Density, VOC in g/L, VOC in wt%, heat capacity, actives, solids, water | Combine ingredient properties using mass or volume fractions. | | Equations | Dynamic and kinematic viscosity, vapor pressure, flash point, initial boiling point, freezing point depression, HLB, settling velocity and time, Q10 and Arrhenius shelf life | Apply a physical relationship with specific assumptions. | | Models and component estimates | Surface tension, solubility risk, auto-ignition temperature, Hildebrand solubility parameter | Combine component data or predictions into screening estimates. | The overview requires **View formulations** permission. Browsing it does not enable calculations in chat. Batch-tool execution retains the organization's activation and audience settings. Property calculations run in the Studio and, where enabled and authorized, through Herman or the formulation MCP tools. ## Read the result before using the number Property results identify their **source**, **method**, **confidence**, **coverage**, and any missing inputs or assumptions. A result may be measured, calculated, estimated, or missing. When a blend measurement is supplied, the reported source identifies it as measured. Coverage matters: some mixing rules calculate from the ingredients with usable data and normalize their weights over that subset. A value with incomplete coverage does not describe the entire formula. HLB coverage is measured over the surfactant portion. Other methods may return no value when required inputs are absent. The model group contains both component-data methods and optional prediction methods. A listed model can be disabled or unavailable; check its status and the result notes. A model name in the catalog is not a promise that it can run for every ingredient or organization. > [!NOTE] > > Flash point and auto-ignition estimates require confirmation by test. Surface tension, solubility, and shelf-life projections depend on the stated assumptions. These calculations do not establish regulatory compliance, full compatibility, or product stability. ## Symbols and units Unless a section says otherwise, equations below assume complete usable input data. | Symbol | Meaning | | - | - | | `wᵢ` | Ingredient mass fraction: wt% divided by 100; fractions sum to 1. | | `φᵢ` | Volume fraction: `(wᵢ/ρᵢ) / Σ(wⱼ/ρⱼ)`. | | `xᵢ` | Mole fraction: `(wᵢ/MWᵢ) / Σ(wⱼ/MWⱼ)` over the components considered by the method. | | `ρᵢ`, `ρ` | Ingredient and blend density, normally in g/mL. | | `MWᵢ` | Molecular weight in g/mol. | | `μ`, `ν` | Dynamic viscosity in mPa·s (equivalent to cP), and kinematic viscosity in cSt. | | `Σ` | Sum over the relevant ingredients. | | `ln`, `exp` | Natural logarithm and exponential. `log10` means base-10 logarithm. | Temperature in a reciprocal-temperature equation is in kelvin: `T(K) = T(°C) + 273.15`. Use ingredient measurements at compatible conditions; the batch conversion tools do not infer a temperature correction. ## Batch and conversion tools These five tools use your supplied quantities and assays. They do not infer ingredient properties from a material name. ### Scale a batch For target batch mass `B` and ingredient percentage `pᵢ`: ```text theme={null} Ingredient mass: mᵢ = B × pᵢ / 100 Ingredient active mass: aᵢ = mᵢ × active_percentᵢ / 100 ``` Supply the batch mass, mass unit, and each ingredient's as-supplied wt%. Supply ingredient active percentages when active-mass results are needed. Composition must total 100 wt%. When a weighing increment is requested, rounding allocates whole increments using the largest remainders. Inspect the reported realized composition after rounding. **Example:** a 200 kg batch with 75 wt% water and 25 wt% stock uses 150 kg water and 50 kg stock. If the stock is 40 wt% active and the water contributes none, the batch contains 20 kg active, or 10 wt%. ### Balance active content For target batch mass `B`, stock activity `a_stock`, diluent activity `a_diluent`, and target activity `a_target`: ```text theme={null} m_stock = B × (a_target − a_diluent) / (a_stock − a_diluent) m_diluent = B − m_stock ``` Use one consistent basis for all three activities, such as wt%. The stock and diluent must have different activities, and the target must be achievable by mixing them. The balance conserves mass and active content; it does not model reaction or evaporation. **Example:** 100 kg at 10 wt% active, made from 40 wt% stock and inactive diluent, needs 25 kg stock and 75 kg diluent. ### Mass conversion The tool uses decimal conversion factors between **g, kg, lb, US ton, and metric ton**: ```text theme={null} 1 kg = 1,000 g 1 lb = 0.45359237 kg 1 US ton = 2,000 lb 1 metric ton = 1,000 kg ``` Specify US ton or metric ton explicitly; an unqualified “ton” is ambiguous. ### Mass and volume conversion ```text theme={null} Volume = mass / density Mass = volume × density ``` Supply the same material's density and the temperatures associated with the density and quantity. Those temperatures must match. Density units include g/mL, g/cm³, kg/L, and kg/m³. Volume units include mL, L, m³, US gallon, and imperial gallon. **Example:** 100 kg at 0.8 kg/L occupies 125 L at the stated temperature. ### Dynamic and kinematic viscosity conversion ```text theme={null} ν(cSt) = μ(cP) / ρ(g/mL) μ(cP) = ν(cSt) × ρ(g/mL) ``` Supply viscosity, conversion direction, and same-material density at matching temperatures. This converts an existing measurement; blend viscosity is calculated separately below. ## Mixing rules: seven property calculators | Property | Equation | Inputs and interpretation | | - | - | - | | Density, g/mL | `ρ = 1 / Σ(wᵢ/ρᵢ)` | Ingredient densities. Assumes additive volumes, with no contraction or expansion on mixing. | | VOC content, g/L | `VOC = Σ(φᵢ × VOCᵢ)` | Ingredient VOC in g/L and densities to calculate volume fractions. | | VOC content, wt% | `VOC_wt% = 100 × Σ[wᵢ × VOCᵢ/(1,000 × ρᵢ)]` | VOC in g/L; density in g/mL. Converts each ingredient's VOC to a mass fraction before combining. | | Heat capacity, J/g·K | `Cp = Σ(wᵢ × Cpᵢ)` | Ingredient heat capacities. Assumes ideal mixing without excess heat capacity. | | Actives content, wt% | `A = Σ(wᵢ × Aᵢ)` | Each ingredient's active percentage on an as-supplied basis. | | Solids content, wt% | `S = Σ(wᵢ × Sᵢ)` | Each ingredient's solids percentage. | | Water content, wt% | `W = Σ(wᵢ × Wᵢ)` | Each ingredient's water percentage. | **Example:** equal masses of two ingredients with densities of 1.0 and 0.8 g/mL give `1 / (0.5/1.0 + 0.5/0.8) = 0.8889 g/mL`. An arithmetic mean of the densities would use the wrong weighting basis. ## Equation-based properties: eleven calculators ### Dynamic and kinematic blend viscosity Both properties offer **Refutas** and **Arrhenius log-mixing** methods. Refutas is the default. Supply ingredient viscosity and density as needed to convert between dynamic and kinematic values. Refutas operates on kinematic viscosity in cSt: ```text theme={null} VBNᵢ = 14.534 × ln(ln(νᵢ + 0.8)) + 10.975 VBN = Σ(wᵢ × VBNᵢ) ν = exp(exp((VBN − 10.975) / 14.534)) − 0.8 μ = ν × ρ ``` The nested logarithm needs a valid input domain: `νᵢ + 0.8` must exceed 1. Arrhenius log-mixing operates on positive dynamic viscosities: ```text theme={null} μ = exp(Σ(wᵢ × ln(μᵢ))) ν = μ / ρ ``` These methods assume Newtonian ingredients at compatible reported temperatures. They do not capture thickener effects, shear dependence, or an interaction term. Thickener and rheology-modifier lines trigger a limitation note. ### Vapor pressure The Raoult–Dalton calculation uses ingredient vapor pressures and molecular weights: ```text theme={null} P_blend = Σ(xᵢ × Pᵢ) ``` Output is in kPa. The implementation treats solids and components above 500 g/mol as non-volatile; non-volatile components with molecular weights still contribute to dilution. Missing evidence is reported in the result. This is an ideal-solution approximation. ### Flash point The default **Liaw mixing rule** solves for temperature `T`: ```text theme={null} Σ[xᵢ × Pᵢ(T) / Pᵢ(T_flash,ᵢ)] = 1 ``` It needs component flash points, molecular weights, vapor pressures, boiling points, and a reference temperature for the pressure curves. The pressure curves are fitted from the supplied vapor pressure and normal boiling point using an exponential relationship in reciprocal temperature. ```text theme={null} bᵢ = ln(101.325 / P_ref,ᵢ) / (1/T_ref − 1/T_boil,ᵢ) Pᵢ(T) = P_ref,ᵢ × exp[−bᵢ × (1/T − 1/T_ref)] ``` Pressures here are in kPa and temperatures are in K. The curve requires a positive reference pressure below atmospheric pressure and a boiling point above the reference temperature. The alternative **Lowest flash point** method reports the lowest known flash point among the volatile components. If Liaw lacks a required pressure curve, the implementation can use this fallback and labels the result accordingly. If the solver cannot find a solution, it returns an unavailable result. Output is °C; confirm by test. ### Initial boiling point The bubble-point calculation solves: ```text theme={null} Σ(xᵢ × Pᵢ(T)) = 101.325 kPa ``` Supply vapor pressures, normal boiling points, molecular weights, and the reference temperature. Output is the predicted initial boiling temperature in °C at atmospheric pressure. It uses the same ideal-solution pressure-curve approach as flash point. It does not describe the full distillation range or azeotropes. ### Freezing point depression ```text theme={null} ΔTf = 1.86 × molality molality = moles of non-water solute / kg of water ``` Supply a water line and solute molecular weights. Output is a temperature **depression in K**, not an absolute freezing point. The method assumes a dilute ideal aqueous solution and a van 't Hoff factor of 1. Dissociation, eutectics, and concentrated-mixture effects are not modeled. ### HLB of the surfactant system ```text theme={null} HLB = Σ(wᵢ × HLBᵢ) / Σ(wᵢ) ``` The sums include only lines assigned a surfactant or emulsifier functional role with usable HLB data. Supply those roles and ingredient HLB values. Output is dimensionless. This describes the surfactant system; it does not calculate the required HLB of the oil phase. ### Settling velocity and time Stokes' law provides two outputs: ```text theme={null} v = g × d² × (ρ_particle − ρ_fluid) / (18 × μ) t_hours = H / abs(v) / 3,600 ``` In these equations, use diameter `d` and fill height `H` in metres, densities in kg/m³, and viscosity in Pa·s. The Studio accepts particle diameter in µm and fill height in cm, and performs the conversions. Velocity is reported in µm/s and time in hours. The calculation needs solid and fluid ingredient lines with densities, particle diameter, and blend dynamic viscosity. It calculates particle and fluid densities separately using inverse mass-weighted density. A negative velocity indicates creaming; matching densities produce no settling-time value. Assumptions are dilute, spherical, non-interacting particles in a Newtonian fluid. The estimate does not capture flocculation or a yield-stress structure. ### Projected shelf life: Q10 and Arrhenius Both calculators require an accelerated-stability observation: days passed at the accelerated temperature, and the intended storage temperature. ```text theme={null} Q10: t_months = (t_accel_days / 30) × Q10^((T_accel_C − T_store_C) / 10) Arrhenius: t_months = (t_accel_days / 30) × exp[(Ea × 1,000 / R) × (1/T_store_K − 1/T_accel_K)] ``` Supply Q10 for the first method and activation energy `Ea` in kJ/mol for the second. The implementation uses `R = 8.314 J/(mol·K)` and 30-day months. Both assume one dominant degradation pathway. They extrapolate an observation; they do not establish shelf life from the recipe alone. Check the scenario values before running a calculation. The current defaults are 25 °C for the scenario temperature, 10 cm for fill height, Q10 of 2, and activation energy of 83 kJ/mol. Defaults are assumptions, not measurements of your product. **Example:** 30 days at 40 °C projected to 20 °C with Q10 = 2 gives `30/30 × 2² = 4 months` under that assumption. ## Models and component estimates: four calculators ### Surface tension The component-data method combines pure-component surface tensions, normally using mole fractions: ```text theme={null} γ_blend = Σ(xᵢ × γᵢ) ``` Output is mN/m. Supply component surface tensions and molecular weights. When molecular weights are incomplete, the implementation falls back to mass weighting and states that basis in the notes. An optional Chemprop method applies the same blend weighting to predicted component values when the model is configured and available. This is a low-confidence screening estimate. Surfactants can dominate actual surface tension; their interfacial effects are not modeled. ### Solubility risk The Chemprop aqueous-solubility method compares each assessed non-water component's concentration with its predicted solubility: ```text theme={null} cᵢ (mol/L) = wᵢ × 1,000 / MWᵢ At risk when: log10(cᵢ) > predicted log10(Sᵢ) ``` It assumes blend density of 1 kg/L and requires water, molecular weights, and usable component solubility predictions. Output is the **count of components** exceeding predicted solubility, with names and unassessed components in the notes. It is not a probability or a solubility measurement. Without a water line, the result notes say aqueous risk was not assessed; a displayed zero in that case does not establish solubility. The method excludes pH, salting, and co-solvent effects. ### Auto-ignition temperature ```text theme={null} T_autoignition = lowest known component auto-ignition temperature ``` The component-data method excludes water and reports °C, identifying the controlling component and missing coverage. Mixtures can ignite below their lowest component value. Confirm by test; do not use this estimate as a safe operating limit. ### Hildebrand solubility parameter The implementation estimates each component's cohesive-energy parameter and then mass-weights the component values: ```text theme={null} Vmᵢ = MWᵢ / ρᵢ δᵢ = sqrt[1,000 × (ΔHvapᵢ − R × T) / Vmᵢ] δ_blend = Σ(wᵢ × δᵢ) ``` Supply heat of vaporization `ΔHvap` in kJ/mol, molecular weight in g/mol, and density in g/mL. Here `Vm` is cm³/mol, `R = 0.008314 kJ/(mol·K)`, and the implementation uses **298.15 K**. Output is MPa½. This is a low-confidence component estimate. The method ignores blend interactions and does not provide Hansen partial parameters or a compatibility verdict. ## When a result is missing or unexpected 1. Check the formula's wt% values and the units of each ingredient input. 2. Check temperature, particle size, fill height, or stability-test conditions required by the selected method. 3. Inspect the reported method, including any fallback, and review coverage and missing ingredients. 4. Check whether an optional prediction model is enabled and available for the inputs. 5. Compare the result with suitable blend measurements before using it for a formulation decision. For organization access or activation questions, see [Merchant Portal troubleshooting](https://docs.plastics.com/merchant-portal/troubleshooting.md). For connected tools, see [MCP for Sellers](https://docs.plastics.com/integrations/mcp/overview.md). This documentation is built and hosted on [Mintlify](https://mintlify.com), a developer documentation platform.