ASTM D5201-05a(2014)

Standard Practice for Calculating Formulation Physical Constants of Paints and Coatings

SIGNIFICANCE AND USE
4.1 Physical constants of paints and coatings are required in all aspects of their formulation, manufacture and use. This practice demonstrates standard methods agreed upon for calculating formulation values for some of these physical constants. The calculations are the same for either metric or inch/pound units.  
4.2 These formula values may not be used to replace measured values required by government regulations unless specifically stated in the governing documents.  
4.3 Some regulations allow compliance determination using formulation data instead of analytical data. This formulation data may not yield the same results as the required analytical method, which could be performed on a sample from any production batch of the coating. In these cases, the user may wish to compare formulation data to analytical data and develop a factor that adjusts for variability of raw materials, variability of production batches, cure volatiles, and variability of the analytical methods.
SCOPE
1.1 This practice covers procedures commonly used in the paint industry to formulate paints and coating materials. It describes procedures for calculating formulation values for weight solids, volume solids, solvent content, volatile organic compound (VOC) content, hazardous air pollutant (HAP) content, and density of liquid paints and coatings. These values are calculated from basic formulation data. These calculations may 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 may not be acceptable for VOC regulatory purposes, depending on the specific wording of the applicable regulation. Some regulations require analysis of the coating. Some rules allow the use of formulation data, however, some adjustments may be needed to the values calculated in this practice before they are used for regulatory purposes (see 4.3).  
1.3 For purposes of this practice, it is assumed that volatile components evaporate and the materials that remain are identified as coating solids. For example, solvents are normally used to adjust viscosity for application and appearance of the coating. Other liquid materials, such as plasticizers, reactive diluents, etc., that are expected to be retained in the dried film to affect the final physical properties should be classified as part of the coating solids. Standards such as Test Methods D2369, D4758, D5403 and Guide D2832 may be used to determine volatile or nonvolatile content of specific components. For purposes of this practice it is assumed that the blended formulation behaves as an ideal solution with no volume change on mixing (see 6.2).  
1.4 Volatile by-products of cross-linking reactions (cure volatiles) are not considered in these calculations since the object of this practice is to define paint physical constants based on formulation information. Variations in raw materials, variations in the production processes, test methods, and test method accuracy are not taken into account in these calculations.  
1.5 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard. However, they may be readily converted into SI units, if required by the user (for example, see Note 4).

General Information

• Status: Historical
• Publication Date: 30-Nov-2014
• ICS: 87.040 - Paints and varnishes
• Technical Committee: D01 - Paint and Related Coatings, Materials, and Applications
• Drafting Committee: D01.24 - Physical Properties of Liquid Paints & Paint Materials

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D5201 − 05a (Reapproved 2014)
Standard Practice for
Calculating Formulation Physical Constants of Paints and
Coatings
This standard is issued under the fixed designation D5201; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope variations in the production processes, test methods, and test
method accuracy are not taken into account in these calcula-
1.1 This practice covers procedures commonly used in the
tions.
paint industry to formulate paints and coating materials. It
1.5 Thevaluesstatedininch-poundunitsaretoberegarded
describes procedures for calculating formulation values for
as standard. The values given in parentheses are mathematical
weight solids, volume solids, solvent content, volatile organic
conversions to SI units that are provided for information only
compound (VOC) content, hazardous air pollutant (HAP)
andarenotconsideredstandard.However,theymaybereadily
content,anddensityofliquidpaintsandcoatings.Thesevalues
converted into SI units, if required by the user (for example,
are calculated from basic formulation data. These calculations
may be related to either as-supplied (unreduced) or as-applied see Note 4).
(reduced) coating materials, including multicomponent types.
2. Referenced Documents
1.2 These calculated, formulation-based values may or may
2.1 ASTM Standards:
not be acceptable for VOC regulatory purposes, depending on
D153Test Methods for Specific Gravity of Pigments
the specific wording of the applicable regulation. Some regu-
D1475Test Method For Density of Liquid Coatings, Inks,
lationsrequireanalysisofthecoating.Somerulesallowtheuse
and Related Products
of formulation data, however, some adjustments may be
D2369Test Method for Volatile Content of Coatings
needed to the values calculated in this practice before they are
D2832GuideforDeterminingVolatileandNonvolatileCon-
used for regulatory purposes (see 4.3).
tent of Paint and Related Coatings
1.3 For purposes of this practice, it is assumed that volatile
D3960PracticeforDeterminingVolatileOrganicCompound
components evaporate and the materials that remain are
(VOC) Content of Paints and Related Coatings
identifiedascoatingsolids.Forexample,solventsarenormally
D4758Test Method for Nonvolatile Content of Latexes
used to adjust viscosity for application and appearance of the
(Withdrawn 2007)
coating. Other liquid materials, such as plasticizers, reactive
D5403Test Methods for Volatile Content of Radiation Cur-
diluents, etc., that are expected to be retained in the dried film
able Materials
to affect the final physical properties should be classified as
E29Practice for Using Significant Digits in Test Data to
part of the coating solids. Standards such as Test Methods
Determine Conformance with Specifications
D2369, D4758, D5403 and Guide D2832 may be used to
2.2 U. S. Environmental Protection Agency Documents:
determine volatile or nonvolatile content of specific compo-
Code of Federal Regulations Title 40 Part 51.100 (s)
nents. For purposes of this practice it is assumed that the
4,5
Definition of VOC Clean Air Act, Section 112
blended formulation behaves as an ideal solution with no
Code of Federal Regulations Title 40Part 63, Subpart
volume change on mixing (see 6.2).
1.4 Volatile by-products of cross-linking reactions (cure
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
volatiles) are not considered in these calculations since the
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
object of this practice is to define paint physical constants
Standards volume information, refer to the standard’s Document Summary page on
based on formulation information. Variations in raw materials,
the ASTM website.
The last approved version of this historical standard is referenced on
www.astm.org.
Available from Superintendent of Documents, U.S. Government Printing
This practice is under the jurisdiction of ASTM Committee D01 on Paint and Office, Washington, DC 20402. They are also available at the EPA website:
Related Coatings, Materials, and Applications and is the direct responsibility of http://www.epa.gov/ttn/atw/coat/coatingscalc.html.
Subcommittee D01.24 on Physical Properties of Liquid Paints and Paint Materials. A list of hazardous air pollutants (HAPs) may be found at the following
Current edition approved Dec. 1, 2014. Published December 2014. Originally website: http://www.epa.gov/ttn/atw/188polls.html. Modifications to this original
approved in 1991. Last previous edition approved in 2010 as D5201–05a (2010). list may be found at the following website: http://www.epa.gov/ttnatw01/
DOI: 10.1520/D5201-05AR14. 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 standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5201 − 05a (2014)
NNNN, Table3 (Default Organic HAP Mass Fraction for per gallon of paint) exclusive of water or solvents that are not
Solvents and Solvent Blends) and Subpart RRRR Table4 VOC.This is a theoretical value that may be an approximation
(Default Organic HAP Mass Fraction for Petroleum Sol- of the VOC content that would be obtained by an analytical
vent Groups) determination, for example, EPA Reference Method 24.
EPAFederal Reference Method24– Determination ofVola- 3.1.7.1 Discussion—Solvent and VOC are not equivalent
tile Matter Content, Water Content, Density Volume terms. See 40 CFR 51·100 (Par·S) for the current EPA
Solids, and Weight Solids, of Surface Coatings definitionofvolatileorganiccompound(VOC)anddescription
EPAFederalReferenceMethod311–AnalysisofHazardous of compounds that are exempt. Ammonia and water are not
Air Pollutant Compound in Paints and Coatings by Direct VOC, as they are not organic compounds.
Injection into a Gas Chromatograph
4. Significance and Use
EPA 450/3-88-018U.S. Environmental Protection Agency
4.1 Physicalconstantsofpaintsandcoatingsarerequiredin
Protocol for Determining the Daily Volatile Organic
all aspects of their formulation, manufacture and use. This
Compound Emission Rate ofAutomobile and Light Duty
practice demonstrates standard methods agreed upon for cal-
Truck Topcoat Operations
culating formulation values for some of these physical con-
3. Terminology stants. The calculations are the same for either metric or
inch/pound units.
3.1 Definitions of Terms Specific to This Standard:
3.1.1 formula density, n—(see Test Method D1475), the 4.2 These formula values may not be used to replace
measured values required by government regulations unless
calculated mass of a unit volume of material at the specified
temperature. specifically stated in the governing documents.
3.1.1.1 Discussion—In this practice, density is expressed in
4.3 Someregulationsallowcompliancedeterminationusing
pounds per U.S. gallon (lb/gal) since this is commonly used in
formulation data instead of analytical data. This formulation
the coatings industry. Where dry materials are concerned,
data may not yield the same results as the required analytical
actual density (not bulk density) should be determined analyti-
method, which could be performed on a sample from any
cally or obtained from supplier information. UseTest Methods
production batch of the coating. In these cases, the user may
D153 where applicable.
wish to compare formulation data to analytical data and
3.1.2 formula HAP content, n—calculated amount based on
develop a factor that adjusts for variability of raw materials,
formula content (such as pounds of HAPper gallon of coating variabilityofproductionbatches,curevolatiles,andvariability
solids).
of the analytical methods.
3.1.2.1 Discussion—This is a theoretical value that may be
5. Calculations
an approximation of the HAP content that would be obtained
5.1 Calculated values should be rounded to the appropriate
by an analytical determination, for example, EPA Reference
number of significant digits in accordance with Practice E29,
Method 311.
GuidelinesforRetainingSignificantFiguresinCalculationand
3.1.3 formula percent volume solids content, n—the calcu-
Reporting of Test Results.
lated volume of nonvolatile material in a formula divided by
5.2 Formula Density (weight per unit volume):
the total volume of the paint material, times 100%.
5.2.1 The formula density (D) can be calculated from the
f
3.1.4 formula percent weight solids content, n—the calcu-
total weight (W) and total volume (V) of the formulation.The
f f
latedweightofnonvolatilematerialinaformuladividedbythe
formulation volume can be calculated from the weight and
total weight of the coating material, times 100%.
density of each ingredient as given by the following equation:
3.1.5 formula solvent content, n—the calculated weight of
D 5 W /V 5 @W 1W 1…W #/@W /D 1W /D 1…W /D #
the solvents in a specific volume of paint (such as pounds of f f f 1 2 n 1 1 2 2 n fn
solventpergallonofpaint),whichisdeterminedbytotalingall 5 sum W / sum W /D (1)
@ # @ #
i i i
solvents present.
where:
3.1.5.1 Discussion—Volatile by-products of cross-linking
n = number of items in the formulation,
reactions (cure volatiles) are not included in the formula
D = formula density, lb/gal (g/L),
f
solvent content.
W = total weight of formula, lb (g),
f
3.1.6 formula volatile density, n—the calculated density of
V = total volume of formula, gal (L),
f
the combined volatile composition (includes VOC, exempt
W = weight of ingredient, lb (g), and
i
solvents, water, ammonia, etc.). D = density of ingredient.
i
3.1.7 formula VOC content, n—calculated amount based
5.2.1.1 An example would be as follows where the weight
upon total formula solvent content, (such as pounds of solvent
(W) and density (D) of each ingredient are known:
Ingredient Weight Density Volume
W, (lb) D, (lb/gal) V, (gal)
1 81.50 7.74 10.530
AvailablefromU.S.GovernmentPrintingOfficeSuperintendentofDocuments,
2 6.10 7.90 0.772
732 N. Capitol St., NW, Mail Stop: SDE, Washington, DC 20401, http://
3 0.40 8.72 0.046
www.access.gpo.gov. Refer to EPA 450/3-88-018 dated December 1988. This
4 12.00 7.65 1.569
protocol makes reference to the paint formulation physical constants for VOC and
Formula 100.00 D 12.917
f
volume solids content.
D5201 − 05a (2014)
D 5100/12.91757.74lb/gal. Calculate percent of solids by volume using one of the
f
following equations, depending on available information.
5.2.2 Ifthedensityofanyoneoftheingredientsinaproduct
5.5.1 Calculate volume percent solids by subtracting the
is unknown, it can be calculated as long as the density of the
volume of solvents from the total volume of paint, as follows:
paint and the other ingredients in that formulation are known.
S 5 total vol of paint 2 vol of solvents / total vol of paint 3100
~~ ! ~ !!
This situation may occur with a resin solution where the v
density and volume of the polymer solids are unknown, as in (5)
the following example:
where:
Weight Density Volume
Ingredient
S = volume percent of solids (nonvolatile)
v
W, (lb) D, (lb/gal) V, (gal)
Polymer solids 50.00 D V
ps ps
or
Solvent A 25.00 6.95 3.60
5.5.2 Calculatevolumepercentsolidsdirectlyifthevolume
Solvent B 25.00 7.18 3.48
Formula 100.00 7.50 V
f of solids and volume of paint are known:
where:
S 5 ~volumeofsolids!/~totalvolumeofpaint! 3100 (6)
V
V = volume of total formula, gal = 100.00/7.50 = 13.3 gal,
f
where:
V = volume of polymer solids, gal = 13.33 − (3.60 + 3.48)
ps
S = volume percent of solids (nonvolatile)
v
= 6.25 gal, and
or,
D = density of polymer solids, lb/gal = 50.00/6.25 = 8.00
ps
lb/gal. 5.5.3 When the volume solids of each ingredient in a
formulationisknown,thevolumesolidsoftheformulationcan
5.3 Formula Solvent (Volatile) Density:
be calculated by totaling the volumes and volume solids of
5.3.1 The density of the solvent (volatile) portion can be
each ingredient as follows:
calculated using the following equation:
5.5.3.1 Calculate the volume (V) of each ingredient from
i
D 5 @V D 1V D 1V D 1…V D #/@V 1V 1V 1…V #
the formula weight (W) of each ingredient, divided by its
s 1 1 2 2 3 3 n n 1 2 3 n
i
density (D):
5 @sum#V D /@sum#V (2) i
i i i
V 5 W /D (7)
i i i
where:
D = density of solvent portion, lb/gal (g/L), 5.5.3.2 Determine the total volume (V) of the formula from
s
f
V = volume of individual solvent, gal (L),
the sum of the volumes of the individual ingredients:
i
D = density of individual solvent, lb/gal (g/L), and
i
V 5 ΣV (8)
f i
n = number of items in the formulation.
5.5.3.3 Formula volume solids content (S ) is calculated in
NOTE 1—The aboveformulapertainstoallsolventsincorporatedinthe
vf
formulation.
the following manner. The volume of each ingredient (V)is
i
NOTE 2—If the weight (W) of the solvents in the formulation is known
multiplied by the volume percent solids of that ingredient (S )
vi
rather than the volume, the overall solvent density can be determined
and the sum of these volume solids is divided by the total
using the alternative equation, as follows:
volume of the formula to give formula volume solids. This is
D 5 Sum W /Sum W /D (3)
~ !
S i i i shown symbolically as follows:
5.4 Formula Weight Percent Solids (Nonvolatile): If the S 5 ~Σ ~S V !!/V (9)
vf vi i f
weight percent solids content of each ingredient is known, the
5.5.3.4 An example would be as follows:
total formulation weight percent solids can be determined by
Ingredient Weight Density D, Total Volume Volume
summing up the weight of solids in each ingredient divided by
W, (lb.) (lb./gal) Volume Solids, % of Solids
the total weight of the paint.
1 7.35 8.00 0.92 31.0 0.29
2 22.41 7.96 2.82 21.5 0.61
5.4.1 Calculate percent of solids by weight as follows:
3 52.85 8.24 6.41 23.8 1.53
4 5.98 7.16 0.84 0.0 . . .
S 5 ~Sum~wt of solids!/~total wt of coating!! 3100 (4)
W
5 6.13 9.27 0.66 100.00 0.66
6 0.28 7.17 0.04 0.0 . . .
5 Σ W S /W
~ ~ !!
i i f
7 5.00 8.14 0.61 33.6 0.20
100.00 12.30 3.29
where:
S = formula weight percent of solids (nonvolatile), %,
W
W = total weight of formula, lb. (g),
f
S 5 total vol of solids, gal / total vol of paint, gal 3100(10)
~ ! ~ !
v
W = weight of ingredient, lb. (g), and
i
where:
S = weight percent solids of ingredient, %.
i
S = volume percent of solids (nonvolatile).
v
5.5 Formula Volume Percent Solids (Nonvolatile): Gener-
ally the volume solids content is calculated by subtracting the 5.6 Formula Total Solvent Content and VOC Content (see
volume of all solvent from the total volume, since the volume
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D5201 − 05a (Reapproved 2010) D5201 − 05a (Reapproved 2014)
Standard Practice for
Calculating Formulation Physical Constants of Paints and
Coatings
This standard is issued under the fixed designation D5201; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*Scope
1.1 This practice covers procedures commonly used in the paint industry to formulate paints and coating materials. It describes
procedures for calculating formulation values for weight solids, volume solids, solvent content, volatile organic compound (VOC)
content, hazardous air pollutant (HAP) content, and density of liquid paints and coatings. These values are calculated from basic
formulation data. These calculations may 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 may not be acceptable for VOC regulatory purposes, depending on the
specific wording of the applicable regulation. Some regulations require analysis of the coating. Some rules allow the use of
formulation data, however, some adjustments may be needed to the values calculated in this practice before they are used for
regulatory purposes (see 4.3).
1.3 For purposes of this practice, it is assumed that volatile components evaporate and the materials that remain are identified
as coating solids. For example, solvents are normally used to adjust viscosity for application and appearance of the coating. Other
liquid materials, such as plasticizers, reactive diluents, etc., that are expected to be retained in the dried film to affect the final
physical properties should be classified as part of the coating solids. Standards such as Test Methods D2369, D4758, D5403 and
Guide D2832 may be used to determine volatile or nonvolatile content of specific components. For purposes of this practice it is
assumed that the blended formulation behaves as an ideal solution with no volume change on mixing (see 6.2).
1.4 Volatile by-products of cross-linking reactions (cure volatiles) are not considered in these calculations since the object of
this practice is to define paint physical constants based on formulation information. Variations in raw materials, variations in the
production processes, test methods, and test method accuracy are not taken into account in these calculations.
1.5 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical
conversions to SI units that are provided for information only and are not considered standard. However, they may be readily
converted into SI units, if required by the user (for example, see Note 4).
2. Referenced Documents
2.1 ASTM Standards:
D153 Test Methods for Specific Gravity of Pigments
D1475 Test Method For Density of Liquid Coatings, Inks, and Related Products
D2369 Test Method for Volatile Content of Coatings
D2832 Guide for Determining Volatile and Nonvolatile Content of Paint and Related Coatings
D3960 Practice for Determining Volatile Organic Compound (VOC) Content of Paints and Related Coatings
D4758 Test Method for Nonvolatile Content of Latexes (Withdrawn 2007)
D5403 Test Methods for Volatile Content of Radiation Curable Materials
E29 Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications
This practice is under the jurisdiction of ASTM Committee D01 on Paint and Related Coatings, Materials, and Applications and is the direct responsibility of
Subcommittee D01.24 on Physical Properties of Liquid Paints and Paint Materials.
Current edition approved Feb. 1, 2010Dec. 1, 2014. Published February 2010December 2014. Originally approved in 1991. Last previous edition approved in 20052010
as D5201 – 05a.D5201 – 05a (2010). DOI: 10.1520/D5201-05AR10.10.1520/D5201-05AR14.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5201 − 05a (2014)
2.2 U. S. Environmental Protection Agency Documents:
4,5
Code of Federal Regulations Title 40 Part 51.100 (s) Definition of VOC Clean Air Act, Section 112
Code of Federal Regulations Title 40 Part 63, Subpart NNNN, Table 3 (Default Organic HAP Mass Fraction for Solvents and
Solvent Blends) and Subpart RRRR Table 4 (Default Organic HAP Mass Fraction for Petroleum Solvent Groups)
EPA Federal Reference Method 24 – Determination of Volatile Matter Content, Water Content, Density Volume Solids, and
Weight Solids, of Surface Coatings
EPA Federal Reference Method 311 – Analysis of Hazardous Air Pollutant Compound in Paints and Coatings by Direct Injection
into a Gas Chromatograph
EPA 450/3-88-018 U.S. Environmental Protection Agency Protocol for Determining the Daily Volatile Organic Compound
Emission Rate of Automobile and Light Duty Truck Topcoat Operations
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 formula density, n—(see Test Method D1475), the calculated mass of a unit volume of material at the specified
temperature.
Available from Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402. They are also available at the EPA website: http://www.epa.gov/
ttn/atw/coat/coatingscalc.html.
A list of hazardous air pollutants (HAPs) may be found at the following website: http://www.epa.gov/ttn/atw/188polls.html. Modifications to this original list 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.
Available 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. This protocol makes reference to the paint formulation physical constants for VOC and volume solids
content.
3.1.1.1 Discussion—
In this practice, density is expressed in pounds per U.S. gallon (lb/gal) since this is commonly used in the coatings industry. Where
dry materials are concerned, actual density (not bulk density) should be determined analytically or obtained from supplier
information. Use Test Methods D153 where applicable.
3.1.2 formula HAP content, n—calculated amount based on formula content (such as pounds of HAP per gallon of coating
solids).
3.1.2.1 Discussion—
This is a theoretical value that may be an approximation of the HAP content that would be obtained by an analytical determination,
for example, EPA Reference Method 311.
3.1.3 formula percent volume solids content, n—the calculated volume of nonvolatile material in a formula divided by the total
volume of the paint material, times 100 %.
3.1.4 formula percent weight solids content, n—the calculated weight of nonvolatile material in a formula divided by the total
weight of the coating material, times 100 %.
3.1.5 formula solvent content, n—the calculated weight of the solvents in a specific volume of paint (such as pounds of solvent
per gallon of paint), which is determined by totaling all solvents present.
3.1.5.1 Discussion—
Volatile by-products of cross-linking reactions (cure volatiles) are not included in the formula solvent content.
3.1.6 formula volatile density, n—the calculated density of the combined volatile composition (includes VOC, exempt solvents,
water, ammonia, etc.).
3.1.7 formula VOC content, n—calculated amount based upon total formula solvent content, (such as pounds of solvent per
gallon of paint) exclusive of water or solvents that are not VOC. This is a theoretical value that may be an approximation of the
VOC content that would be obtained by an analytical determination, for example, EPA Reference Method 24.
3.1.7.1 Discussion—
Solvent and VOC are not equivalent terms. See 40 CFR 51·100 (Par·S) for the current EPA definition of volatile organic compound
(VOC) and description of compounds that are exempt. Ammonia and water are not VOC, as they are not organic compounds.
D5201 − 05a (2014)
4. Significance and Use
4.1 Physical constants of paints and coatings are required in all aspects of their formulation, manufacture and use. This practice
demonstrates standard methods agreed upon for calculating formulation values for some of these physical constants. The
calculations are the same for either metric or inch/pound units.
4.2 These formula values may not be used to replace measured values required by government regulations unless specifically
stated in the governing documents.
4.3 Some regulations allow compliance determination using formulation data instead of analytical data. This formulation data
may not yield the same results as the required analytical method, which could be performed on a sample from any production batch
of the coating. In these cases, the user may wish to compare formulation data to analytical data and develop a factor that adjusts
for variability of raw materials, variability of production batches, cure volatiles, and variability of the analytical methods.
5. Calculations
5.1 Calculated values should be rounded to the appropriate number of significant digits in accordance with Practice E29,
Guidelines for Retaining Significant Figures in Calculation and Reporting of Test Results.
5.2 Formula Density (weight per unit volume):
5.2.1 The formula density (D ) can be calculated from the total weight (W ) and total volume (V ) of the formulation. The
f f f
formulation volume can be calculated from the weight and density of each ingredient as given by the following equation:
D 5 W /V 5 W 1W 1…W / W /D 1W /D 1…W /D 5 sum W / sum W /D (1)
@ # @ # @ # @ #
f f f 1 2 n 1 1 2 2 n fn i i i
where:
n = number of items in the formulation,
D = formula density, lb/gal (g/L),
f
W = total weight of formula, lb (g),
f
V = total volume of formula, gal (L),
f
W = weight of ingredient, lb (g), and
i
D = density of ingredient.
i
where:
n = number of items in the formulation,
D = formula density, lb/gal (g/L),
f
W = total weight of formula, lb (g),
f
V = total volume of formula, gal (L),
f
W = weight of ingredient, lb (g), and
i
D = density of ingredient.
i
5.2.1.1 An example would be as follows where the weight (W) and density (D) of each ingredient are known:
Ingredient Weight Density Volume
W, (lb) D, (lb/gal) V, (gal)
1 81.50 7.74 10.530
2 6.10 7.90 0.772
3 0.40 8.72 0.046
4 12.00 7.65 1.569
Formula 100.00 D 12.917
f
Ingredient Weight Density Volume
W, (lb) D, (lb/gal) V, (gal)
1 81.50 7.74 10.530
2 6.10 7.90 0.772
3 0.40 8.72 0.046
4 12.00 7.65 1.569
Formula 100.00 D 12.917
f
D 5100/12.91757.74 lb/gal.
f
5.2.2 If the density of any one of the ingredients in a product is unknown, it can be calculated as long as the density of the paint
and the other ingredients in that formulation are known. This situation may occur with a resin solution where the density and
volume of the polymer solids are unknown, as in the following example:
Weight Density Volume
Ingredient
W, (lb) D, (lb/gal) V, (gal)
Polymer solids 50.00 D V
ps ps
Solvent A 25.00 6.95 3.60
Solvent B 25.00 7.18 3.48
Formula 100.00 7.50 V
f
D5201 − 05a (2014)
Weight Density Volume
Ingredient
W, (lb) D, (lb/gal) V, (gal)
Polymer solids 50.00 D V
ps ps
Solvent A 25.00 6.95 3.60
Solvent B 25.00 7.18 3.48
Formula 100.00 7.50 V
f
where:
V = volume of total formula, gal = 100.00/7.50 = 13.3 gal,
f
V = volume of polymer solids, gal = 13.33 − (3.60 + 3.48) = 6.25 gal, and
ps
D = density of polymer solids, lb/gal = 50.00/6.25 = 8.00 lb/gal.
ps
5.3 Formula Solvent (Volatile) Density:
5.3.1 The density of the solvent (volatile) portion can be calculated using the following equation:
D 5 @V D 1V D 1V D 1…V D #/@V 1V 1V 1…V # 5 @sum# V D /@sum# V (2)
s 1 1 2 2 3 3 n n 1 2 3 n i i i
where:
D = density of solvent portion, lb/gal (g/L),
s
V = volume of individual solvent, gal (L),
i
D = density of individual solvent, lb/gal (g/L), and
i
n = number of items in the formulation.
where:
D = density of solvent portion, lb/gal (g/L),
s
V = volume of individual solvent, gal (L),
i
D = density of individual solvent, lb/gal (g/L), and
i
n = number of items in the formulation.
NOTE 1—The above formula pertains to all solvents incorporated in the formulation.
NOTE 2—If the weight (W) of the solvents in the formulation is known rather than the volume, the overall solvent density can be determined using
the alternative equation, as follows:
D 5 Sum W /Sum W /D (3)
~ !
S i i i
5.4 Formula Weight Percent Solids (Nonvolatile): If the weight percent solids content of each ingredient is known, the total
formulation weight percent solids can be determined by summing up the weight of solids in each ingredient divided by the total
weight of the paint.
5.4.1 Calculate percent of solids by weight as follows:
S 5 ~Sum~wt of solids!/~total wt of coating!! 3100 (4)
W
5~Σ~W S !!/W
i i f
where:
S = formula weight percent of solids (nonvolatile), %,
W
W = total weight of formula, lb. (g),
f
W = weight of ingredient, lb. (g), and
i
S = weight percent solids of ingredient, %.
i
where:
S = formula weight percent of solids (nonvolatile), %,
W
W = total weight of formula, lb. (g),
f
W = weight of ingredient, lb. (g), and
i
S = weight percent solids of ingredient, %.
i
5.5 Formula Volume Percent Solids (Nonvolatile): Generally the volume solids content is calculated by subtracting the volume
of all solvent from the total volume, since the volume of the solvent portion is usually more readily available than the volume of
solid materials. The volume of the solvent portion may be obtained directly from the formula data or determined by dividing the
weight (W) by the density (D) of each solvent. Calculate percent of solids by volume using one of the following equations,
depending on available information.
5.5.1 Calculate volume per
...