Designation: D5201 − 05a (Reapproved 2014)Standard Practice forCalculating Formulation Physical Constants of Paints andCoatings1This standard is issued under the fixed designation D5201; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers procedures commonly used in thepaint industry to formulate paints and coating materials. Itdescribes procedures for calculating formulation values forweight solids, volume solids, solvent content, volatile organiccompound (VOC) content, hazardous air pollutant (HAP)content, and density of liquid paints and coatings. These valuesare calculated from basic formulation data. These calculationsmay be related to either as-supplied (unreduced) or as-applied(reduced) coating materials, including multicomponent types.1.2 These calculated, formulation-based values may or maynot be acceptable for VOC regulatory purposes, depending onthe specific wording of the applicable regulation. Some regu-lations require analysis of the coating. Some rules allow the useof formulation data, however, some adjustments may beneeded to the values calculated in this practice before they areused for regulatory purposes (see 4.3).1.3 For purposes of this practice, it is assumed that volatilecomponents evaporate and the materials that remain areidentified as coating solids. For example, solvents are normallyused to adjust viscosity for application and appearance of thecoating. Other liquid materials, such as plasticizers, reactivediluents, etc., that are expected to be retained in the dried filmto affect the final physical properties should be classified aspart of the coating solids. Standards such as Test MethodsD2369, D4758, D5403 and Guide D2832 may be used todetermine volatile or nonvolatile content of specific compo-nents. For purposes of this practice it is assumed that theblended formulation behaves as an ideal solution with novolume change on mixing (see 6.2).1.4 Volatile by-products of cross-linking reactions (curevolatiles) are not considered in these calculations since theobject of this practice is to define paint physical constantsbased on formulation information. Variations in raw materials,variations in the production processes, test methods, and testmethod accuracy are not taken into account in these calcula-tions.1.5 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard. However, they may be readilyconverted into SI units, if required by the user (for example,see Note 4).2. Referenced Documents2.1 ASTM Standards:2D153 Test Methods for Specific Gravity of PigmentsD1475 Test Method For Density of Liquid Coatings, Inks,and Related ProductsD2369 Test Method for Volatile Content of CoatingsD2832 Guide for Determining Volatile and Nonvolatile Con-tent of Paint and Related CoatingsD3960 Practice for DeterminingVolatile Organic Compound(VOC) Content of Paints and Related CoatingsD4758 Test Method for Nonvolatile Content of Latexes(Withdrawn 2007)3D5403 Test Methods for Volatile Content of Radiation Cur-able MaterialsE29 Practice for Using Significant Digits in Test Data toDetermine Conformance with Specifications2.2 U. S. Environmental Protection Agency Documents:Code of Federal Regulations Title 40 Part 51.100 (s)Definition of VOC Clean Air Act, Section 1124,5Code of Federal Regulations Title 40 Part 63, Subpart1This practice is under the jurisdiction of ASTM Committee D01 on Paint andRelated Coatings, Materials, and Applications and is the direct responsibility ofSubcommittee D01.24 on Physical Properties of Liquid Paints and Paint Materials.Current edition approved Dec. 1, 2014. Published December 2014. Originallyapproved in 1991. Last previous edition approved in 2010 as D5201 – 05a (2010).DOI: 10.1520/D5201-05AR14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.4Available from Superintendent of Documents, U.S. Government PrintingOffice, Washington, DC 20402. They are also available at the EPA website:http://www.epa.gov/ttn/atw/coat/coatingscalc.html.5A list of hazardous air pollutants (HAPs) may be found at the followingwebsite: http://www.epa.gov/ttn/atw/188polls.html. Modifications to this originallist may be found at the following website: http://www.epa.gov/ttnatw01/atwsmod.html or at the Code of Federal Regulations, Title 40, Part 63, Subpart C.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1NNNN, Table 3 (Default Organic HAP Mass Fraction forSolvents and Solvent Blends) and Subpart RRRR Table 4(Default Organic HAP Mass Fraction for Petroleum Sol-vent Groups)4EPA Federal Reference Method 24 – Determination of Vola-tile Matter Content, Water Content, Density VolumeSolids, and Weight Solids, of Surface Coatings4EPAFederal Reference Method 311 –Analysis of HazardousAir Pollutant Compound in Paints and Coatings by DirectInjection into a Gas Chromatograph4EPA 450/3-88-018 U.S. Environmental Protection AgencyProtocol for Determining the Daily Volatile OrganicCompound Emission Rate of Automobile and Light DutyTruck Topcoat Operations63. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 formula density, n—(see Test Method D1475), thecalculated mass of a unit volume of material at the specifiedtemperature.3.1.1.1 Discussion—In this practice, density is expressed inpounds per U.S. gallon (lb/gal) since this is commonly used inthe coatings industry. Where dry materials are concerned,actual density (not bulk density) should be determined analyti-cally or obtained from supplier information. Use Test MethodsD153 where applicable.3.1.2 formula HAP content, n—calculated amount based onformula content (such as pounds of HAP per gallon of coatingsolids).3.1.2.1 Discussion—This is a theoretical value that may bean approximation of the HAP content that would be obtainedby an analytical determination, for example, EPA ReferenceMethod 311.3.1.3 formula percent volume solids content, n—the calcu-lated volume of nonvolatile material in a formula divided bythe total volume of the paint material, times 100 %.3.1.4 formula percent weight solids content, n—the calcu-lated weight of nonvolatile material in a formula divided by thetotal weight of the coating material, times 100 %.3.1.5 formula solvent content, n—the calculated weight ofthe solvents in a specific volume of paint (such as pounds ofsolvent per gallon of paint), which is determined by totaling allsolvents present.3.1.5.1 Discussion—Volatile by-products of cross-linkingreactions (cure volatiles) are not included in the formulasolvent content.3.1.6 formula volatile density, n—the calculated density ofthe combined volatile composition (includes VOC, exemptsolvents, water, ammonia, etc.).3.1.7 formula VOC content, n—calculated amount basedupon total formula solvent content, (such as pounds of solventper gallon of paint) exclusive of water or solvents that are notVOC. This is a theoretical value that may be an approximationof the VOC content that would be obtained by an analyticaldetermination, for example, EPA Reference Method 24.3.1.7.1 Discussion—Solvent and VOC are not equivalentterms. See 40 CFR 51·100 (Par·S) for the current EPAdefinition of volatile organic compound (VOC) and descriptionof compounds that are exempt. Ammonia and water are notVOC, as they are not organic compounds.4. Significance and Use4.1 Physical constants of paints and coatings are required inall aspects of their formulation, manufacture and use. Thispractice demonstrates standard methods agreed upon for cal-culating formulation values for some of these physical con-stants. The calculations are the same for either metric orinch/pound units.4.2 These formula values may not be used to replacemeasured values required by government regulations unlessspecifically stated in the governing documents.4.3 Some regulations allow compliance determination usingformulation data instead of analytical data. This formulationdata may not yield the same results as the required analyticalmethod, which could be performed on a sample from anyproduction batch of the coating. In these cases, the user maywish to compare formulation data to analytical data anddevelop a factor that adjusts for variability of raw materials,variability of production batches, cure volatiles, and variabilityof the analytical methods.5. Calculations5.1 Calculated values should be rounded to the appropriatenumber of significant digits in accordance with Practice E29,Guidelines for Retaining Significant Figures in Calculation andReporting of Test Results.5.2 Formula Density (weight per unit volume):5.2.1 The formula density (Df) can be calculated from thetotal weight (Wf) and total volume (Vf) of the formulation. Theformulation volume can be calculated from the weight anddensity of each ingredient as given by the following equation:Df5 Wf/Vf5 @W11W21… Wn#/@W1/D11W2/D21… Wn/Dfn#5 @sum# Wi/@sum# Wi/Di(1)where:n = number of items in the formulation,Df= formula density, lb/gal (g/L),Wf= total weight of formula, lb (g),Vf= total volume of formula, gal (L),Wi= weight of ingredient, lb (g), andDi= density of ingredient.5.2.1.1 An example would be as follows where the weight(W) and density (D) of each ingredient are known:Ingredient WeightW, (lb)DensityD, (lb/gal)VolumeV, (gal)1 81.50 7.74 10.5302 6.10 7.90 0.7723 0.40 8.72 0.0464 12.00 7.65 1.569Formula 100.00 Df12.9176Available from U.S. Government Printing Office Superintendent of Documents,732 N. Capitol St., NW, Mail Stop: SDE, Washington, DC 20401, http://www.access.gpo.gov. Refer to EPA 450/3-88-018 dated December 1988. Thisprotocol makes reference to the paint formulation physical constants for VOC andvolume solids content.D5201 − 05a (2014)2Df5100/12.91757.74 lb/gal.5.2.2 If the density of any one of the ingredients in a productis unknown, it can be calculated as long as the density of thepaint and the other ingredients in that formulation are known.This situation may occur with a resin solution where thedensity and volume of the polymer solids are unknown, as inthe following example:IngredientWeightW, (lb)DensityD, (lb/gal)VolumeV, (gal)Polymer solids 50.00 DpsVpsSolvent A 25.00 6.95 3.60Solvent B 25.00 7.18 3.48Formula 100.00 7.50 Vfwhere:Vf= volume of total formula, gal = 100.00/7.50 = 13.3 gal,Vps= volume of polymer solids, gal = 13.33 − (3.60 + 3.48)= 6.25 gal, andDps= density of polymer solids, lb/gal = 50.00/6.25 = 8.00lb/gal.5.3 Formula Solvent (Volatile) Density:5.3.1 The density of the solvent (volatile) portion can becalculated using the following equation:Ds5 @V1D11V2D21V3D31…VnDn#/@V11V21V31…Vn#5 @sum# ViDi/@sum# Vi(2)where:Ds= density of solvent portion, lb/gal (g/L),Vi= volume of individual solvent, gal (L),Di= density of individual solvent, lb/gal (g/L), andn = number of items in the formulation.NOTE 1—The above formula pertains to all solvents incorporated in theformulation.NOTE 2—If the weight (W) of the solvents in the formulation is knownrather than the volume, the overall solvent density can be determinedusing the alternative equation, as follows:DS5 Sum Wi/Sum~Wi/Di! (3)5.4 Formula Weight Percent Solids (Nonvolatile): If theweight percent solids content of each ingredient is known, thetotal formulation weight percent solids can be determined bysumming up the weight of solids in each ingredient divided bythe total weight of the paint.5.4.1 Calculate percent of solids by weight as follows:SW5 ~Sum~wt of solids!/~total wt of coating!! 3100 (4)5~Σ~WiSi!!/Wfwhere:SW= formula weight percent of solids (nonvolatile), %,Wf= total weight of formula, lb. (g),Wi= weight of ingredient, lb. (g), andSi= weight percent solids of ingredient, %.5.5 Formula Volume Percent Solids (Nonvolatile): Gener-ally the volume solids content is calculated by subtracting thevolume of all solvent from the total volume, since the volumeof the solvent portion is usually more readily available than thevolume of solid materials. The volume of the solvent portionmay be obtained directly from the formula data or determinedby dividing the weight (W) by the density (D) of each solvent.Calculate percent of solids by volume using one of thefollowing equations, depending on available information.5.5.1 Calculate volume percent solids by subtracting thevolume of solvents from the total volume of paint, as follows:Sv5 ~~total vol of paint 2 vol of solvents!/~total vol of paint!! 3100(5)where:Sv= volume percent of solids (nonvolatile)or5.5.2 Calculate volume percent solids directly if the volumeof solids and volume of paint are known:SV5 ~volume of solids!/~total volume of paint! 3100 (6)where:Sv= volume percent of solids (nonvolatile)or,5.5.3 When the volume solids of each ingredient in aformulation is known, the volume solids of the formulation canbe calculated by totaling the volumes and volume solids ofeach ingredient as follows:5.5.3.1 Calculate the volume (Vi) of each ingredient fromthe formula weight (Wi) of each ingredient, divided by itsdensity (Di):Vi5 Wi/Di(7)5.5.3.2 Determine the total volume (Vf) of the formula fromthe sum of the volumes of the individual ingredients:Vf5 ΣVi(8)5.5.3.3 Formula volume solids content (Svf) is calculated inthe following manner. The volume of each ingredient (Vi)ismultiplied by the volume percent solids of that ingredient (Svi)and the sum of these volume solids is divided by the totalvolume of the formula to give formula volume solids. This isshown symbolically as follows:Svf5 ~Σ ~SviVi!!/Vf(9)5.5.3.4 An example would be as follows:Ingredient WeightW, (lb.)Density D,(lb./gal)TotalVolumeVolumeSolids, %Volumeof Solids1 7.35 8.00 0.92 31.0 0.292 22.41 7.96 2.82 21.5 0.613 52.85 8.24 6.41 23.8 1.534 5.98 7.16 0.84 0.0 . . .5 6.13 9.27 0.66 100.00 0.666 0.28 7.17 0.04 0.0 . . .7 5.00 8.14 0.61 33.6 0.20100.00 12.30 3.29Sv5 ~total vol of solids, gal!/~total vol of paint, gal! 3100(10)where:Sv= volume percent of solids (nonvolatile).5.6 Formula Total Solvent Content and VOC Content (see3.1.7): In this practice VOC content is expressed in four ways:(1) Mass of VOC per unit volume of coating less water and lessexempt volatile compounds, (2) Mass of VOC per unit volumeof coating solids, (3) Mass of VOC per unit mass of solids, and(4) Mass of VOC per unit volume of coating including waterD5201 − 05a (2014)3and exempt volatile compou