Cálculo de NORMA

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Universidade de São Paulo Instituto de Geociências 
___________________________________________________________________________ 
 
São Paulo – 2006 Estêvão Inácio Sumburane 
1 
Calculation of a Norm from a Bulk Chemical Analysis 
This Excel spreadsheet program will calculate a norm for you, but detailed instructions for a 
basic norm calculation are below. 
A norm is essentially a set of idealized synthetic minerals that are calculated from a bulk 
chemical analysis of a rock for comparison purposes. Norms are usually calculated for 
volcanic rocks which have glass and/or exceedingly small crystals that make it difficult to 
determine a mode, and for metamorphosed igneous rocks that no longer have the original 
igneous mineralogy. The normative minerals can be thought of as representing the 
minerals that could potentially crystallize if the rock were cooled under perfect equilibrium 
dry conditions. The assemblages of normative minerals are based largely on reality. In real 
rocks the mineral pairs: 
quartz and Mg-rich olivine 
quartz and nepheline 
Al-silicates and augite 
orthopyroxene and nepheline, 
are usually mutually exclusive. The mutually exclusive normative mineral pairs are similar: 
quartz and olivine 
quartz and nepheline 
corundum and diopside 
orthopyroxene and nepheline. 
 
These mutually exclusive mineral pairs result in the four common normative assemblages: 
 
Norm assemblages Meaning 
Quartz, corundum, OPX: Silica-saturated, peraluminous, subalkaline 
Quartz, diopside, OPX: Silica-saturated, subaluminous, subalkaline 
Olivine, diopside, OPX: Silica-undersaturated, subaluminous, subalkaline 
Olivine, diopside, nepheline: Silica-undersaturated, subaluminous, peralkaline 
Universidade de São Paulo Instituto de Geociências 
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São Paulo – 2006 Estêvão Inácio Sumburane 
2 
NORM CALCULATION PROCEDURE 
The following procedure has been abridged for the most common rocks, omitting many 
calculations for unusual rocks. For example, the procedures to calculate normative leucite 
in strongly silica-undersaturated rocks, aegirine in alumina-undersaturated alkalic rocks, or 
hematite in oxidized rocks have been omitted. The procedure below also departs from the 
original CIPW norm in that the pyroxenes, plagioclase, and olivine are calculated as their 
solid solutions rather than as end member components. You must do all calculations to at 
least five decimal places or severe rounding errors will result. 
1) Use only the eleven major element oxides, for which the gram formula weights are: 
SiO2 60.0843 
TiO2 79.8988 
Al2O3 101.9613 
Fe2O3 159.6922 
FeO 71.8464 
MnO 70.9374 
MgO 40.3044 
CaO 56.0794 
Na2O 61.9789 
K2O 94.1960 
P2O5 141.9445 
2) Take the oxide weight percents in the chemical analysis and divide them by their 
respective formula weights to give molar oxide proportions. Use these molar oxide 
proportions in all subsequent calculations. 
3) Add MnO to FeO. MnO is now zero. The combined FeO and MnO will now be called 
FeO. 
Universidade de São Paulo Instituto de Geociências 
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São Paulo – 2006 Estêvão Inácio Sumburane 
3 
4) Apatite (Ap): Multiply P2O5 times 3.33 and subtract this number from CaO. P2O5 
represents 2/3 of an apatite molecule, so multiply P2O5 times 2/3, and put this number in 
Apatite. P2O5 is now zero. 
5) Ilmenite (Ilm): Subtract TiO2 from FeO. Put the TiO2 value in ilmenite. TiO2 is now zero. 
6) Magnetite (Mt): Subtract Fe2O3 from FeO. Put the Fe2O3 value in magnetite. Fe2O3 is 
now zero. 
7) Orthoclase (Or): Subtract K2O from Al2O3. Put the K2O value in orthoclase. K2O is now 
zero. 
8) Albite (Ab) [Provisional]: Subtract Na2O from Al2O3. Put the Na2O value in albite. Retain 
the Na2O value for possible normative nepheline. 
9) Anorthite (An): 
a) If CaO is more than Al2O3, then subtract Al2O3 from CaO. Put all Al2O3 into anorthite. 
Al2O3 is now zero. 
b) If Al2O3 is more than CaO, then subtract CaO from Al2O3. Put all CaO into anorthite. CaO 
is now zero. 
10) Corundum (Cor): If Al2O3 is not zero, put the remaining Al2O3 into Corundum. Diopside 
and Al2O3 are now zero. 
11) Calculate the current ratio of Mg/(Mg+Fe+2). This ratio is called Mg' and will be the 
Mg/(Mg+Fe+2) ratio for all normative silicates. 
Mg' = MgO/(MgO+FeO) 
12) Calculate the mean formula weight of the remaining FeO and MgO. This combined Fe-
Mg oxide called FMO will be used in subsequent calculations. 
Formula weight of FMO = (Mg'*40.3044)+((1-Mg')*71.8464) 
Universidade de São Paulo Instituto de Geociências 
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São Paulo – 2006 Estêvão Inácio Sumburane 
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13) Add FeO and MgO to get FMO. 
14) Diopside (Di): If CaO is not zero, subtract CaO from FMO. Put all CaO into diopside. 
CaO is now zero. 
15) Hypersthene (Hy) [Provisional]: Put all remaining FMO into hypersthene. Retain the 
FMO value for the possible calculation of normative olivine. 
16) Calculate the amount of SiO2 needed for all of the normative silicate minerals listed 
above, allotting SiO2 as follows: 
Orthoclase * 6 = needed SiO2 for each Orthoclase 
Albite * 6 = needed SiO2 for each Albite 
Anorthite * 2 = needed SiO2 for each Anorthite 
Diopside * 2 = needed SiO2 for each Diopside 
Hypersthene * 1 = needed SiO2 for each Hypersthene 
Sum the five SiO2 values just calculated, and call this number pSi for provisional SiO2. 
17) Quartz (Qz): If there is enough silica to make all five minerals then the rock is quartz-
normative. Otherwise there is no quartz in the norm and silica to make the rest of the 
silicates must come from other sources. 
a) If pSi calculated in step 16 is less than SiO2, then there is excess silica. Subtract pSi 
from SiO2, and put excess SiO2 in quartz. SiO2, Nepheline, and olivine are now zero. Skip 
to step 20. 
b) If pSi calculated in step 16 is more than SiO2, then the rock is silica deficient. Proceed to 
step 18. 
18) Olivine (Ol), Hypersthene (Hy): If pSi calculated in step 16 is more than SiO2, then there 
is an SiO2 deficit. Quartz is now zero. Calculate a new pSi as in step 16, omitting 
hypersthene. 
Orthoclase * 6 = needed SiO2 for each Orthoclase 
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Albite * 6 = needed SiO2 for each Albite 
Anorthite * 2 = needed SiO2 for each Anorthite 
Diopside * 2 = needed SiO2 for each Diopside 
Sum the four SiO2 values just calculated to get a new value of pSi. Subtract the new 
pSi from SiO2 to get the amount of SiO2 availablefor olivine and hypersthene, called 
aSi. 
a) If FMO is greater than or equal to 2 times aSi, then put all FMO in olivine. FMO and 
hypersthene are now zero. Proceed to step 19. 
b) If FMO is less than 2 times aSi, then nepheline is zero. Calculate the amount of 
hypersthene and olivine as follows: 
Hypersthene = ((2 * aSi) - FMO) 
Olivine = (FMO - Hypersthene) 
Skip to step 20. 
19) Nepheline (Ne), Albite (Ab): If you reached this step, then turning hypersthene into 
olivine in step 18a did not yield enough silica to make Or, Ab, An, Di, and Ol. Calculate a 
new pSi value as in step 16, omitting hypersthene and albite. 
Orthoclase * 6 = needed SiO2 for each Orthoclase 
Anorthite * 2 = needed SiO2 for each Anorthite 
Diopside * 2 = needed SiO2 for each Diopside 
Olivine * 0.5 = needed SiO2 for each Olivine 
Sum the three SiO2 values just calculated to get a new value of pSi. Subtract this pSi 
from SiO2 to get a new value of aSi, which is the amount of SiO2 available for albite 
and nepheline. 
Albite = (aSi-(2*Na2O))/4 
Nepheline = Na2O-Albite 
20) Multiply orthoclase, albite, and nepheline by two. Divide olivine by two. 
Universidade de São Paulo Instituto de Geociências 
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21) Calculate An', which is the Ca/(Ca+Na) ratio in normative plagioclase: 
An' = Anorthite/(Anorthite+Albite) 
22) Plagioclase (Plag): Add albite to anorthite to make plagioclase. Retain the albite value. 
23) Calculate the formula weight of plagioclase, using the An' value from step 21. 
Formula weight Plag = (An'*278.2093)+((1-An')*262.2230) 
24) Multiply all of the normative mineral values by their respective formula weights. The 
formula weight of FMO is from step 12. 
Qz 60.0843 SiO2 
Or 278.3315 KAlSi3O8 
Plag Calculated in step 23 (Ca,Na)(Al,Si)4O8 
Cor 101.9613 Al2O3 
Ne 142.0544 NaAlSiO4 
Di 176.2480 + formula weight of FMO Ca(Fe,Mg)Si2O6 
Hy 60.0843 + formula weight of FMO (Fe,Mg)SiO3 
Ol 60.0843 + (2 * formula weight of FMO) (Fe,Mg)2SiO4 
Mt 231.5386 Fe3O4 
Ilm 151.7452 FeTiO3 
Ap 504.3125 Ca5(PO4)3F 
25) This is your weight norm. This would usually be published along with four other useful 
parameters: 
Total: The sum of all mineral weights in the norm, calculated in step 24. Within rounding 
error the Total should be the same as the original total of the weight % of the oxides 
from the chemical analysis. 
Mg'%: 100*Mg' From step 11. 
An'%: 100*An' from step 21. 
DI: The Differentiation Index of Thornton and Tuttle (1960). This is the weight ratio: 
Universidade de São Paulo Instituto de Geociências 
___________________________________________________________________________ 
 
São Paulo – 2006 Estêvão Inácio Sumburane 
7 
(Qz+Or+Ab+Ne)/Total. Ab is albite from step 20 times 262.2230. 
26) The weight norm is the way norms are usually expressed. If you want to compare 
norms to modes (which are volume fractions) you should divide each normative mineral by 
its density and normalize the Total back to 100%. Mineral densities can be gotten from 
mineralogy texts, the CRC Handbook of Chemistry and Physics, or elsewhere. The density 
of plagioclase and the Fe-Mg silicates with intermediate solid solutions can be found in 
tables or figures in mineralogy texts, or equations derived from them. 
27) Remember that this Excel spreadsheet program can calculate norms for you. 
 
 
 
Calculation of a Norm from a Bulk Chemical Analysis 
This Excel spreadsheet program will calculate a norm for you, but detailed instructions for a 
basic norm calculation are below. 
A norm is essentially a set of idealized synthetic minerals that are calculated from a bulk 
chemical analysis of a rock for comparison purposes. Norms are usually calculated for 
volcanic rocks which have glass and/or exceedingly small crystals that make it difficult to 
determine a mode, and for metamorphosed igneous rocks that no longer have the original 
igneous mineralogy. The normative minerals can be thought of as representing the 
minerals that could potentially crystallize if the rock were cooled under perfect equilibrium 
dry conditions. The assemblages of normative minerals are based largely on reality. In real 
rocks the mineral pairs: 
quartz and Mg-rich olivine 
quartz and nepheline 
Al-silicates and augite 
orthopyroxene and nepheline, 
are usually mutually exclusive. The mutually exclusive normative mineral pairs are similar: 
Universidade de São Paulo Instituto de Geociências 
___________________________________________________________________________ 
 
São Paulo – 2006 Estêvão Inácio Sumburane 
8 
quartz and olivine 
quartz and nepheline 
corundum and diopside 
orthopyroxene and nepheline. 
 
These mutually exclusive mineral pairs result in the four common normative assemblages: 
 
Norm assemblages Meaning 
Quartz, corundum, OPX: Silica-saturated, peraluminous, subalkaline 
Quartz, diopside, OPX: Silica-saturated, subaluminous, subalkaline 
Olivine, diopside, OPX: Silica-undersaturated, subaluminous, subalkaline 
Olivine, diopside, nepheline: Silica-undersaturated, subaluminous, peralkaline 
NORM CALCULATION PROCEDURE 
The following procedure has been abridged for the most common rocks, omitting many 
calculations for unusual rocks. For example, the procedures to calculate normative leucite 
in strongly silica-undersaturated rocks, aegirine in alumina-undersaturated alkalic rocks, or 
hematite in oxidized rocks have been omitted. The procedure below also departs from the 
original CIPW norm in that the pyroxenes, plagioclase, and olivine are calculated as their 
solid solutions rather than as end member components. You must do all calculations to at 
least five decimal places or severe rounding errors will result. 
1) Use only the eleven major element oxides, for which the gram formula weights are: 
SiO2 60.0843 
TiO2 79.8988 
Al2O3 101.9613 
Fe2O3 159.6922 
FeO 71.8464 
MnO 70.9374 
MgO 40.3044 
Universidade de São Paulo Instituto de Geociências 
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CaO 56.0794 
Na2O 61.9789 
K2O 94.1960 
P2O5 141.9445 
2) Take the oxide weight percents in the chemical analysis and divide them by their 
respective formula weights to give molar oxide proportions. Use these molar oxide 
proportions in all subsequent calculations. 
3) Add MnO to FeO. MnO is now zero. The combined FeO and MnO will now be called 
FeO. 
4) Apatite (Ap): Multiply P2O5 times 3.33 and subtract this number from CaO. P2O5 
represents 2/3 of an apatite molecule, so multiply P2O5 times 2/3, and put this number in 
Apatite. P2O5 is now zero. 
5) Ilmenite (Ilm): Subtract TiO2 from FeO. Put the TiO2 value in ilmenite. TiO2 is now zero. 
6) Magnetite (Mt): Subtract Fe2O3 from FeO. Put the Fe2O3 value in magnetite. Fe2O3 is 
nowzero. 
7) Orthoclase (Or): Subtract K2O from Al2O3. Put the K2O value in orthoclase. K2O is now 
zero. 
8) Albite (Ab) [Provisional]: Subtract Na2O from Al2O3. Put the Na2O value in albite. Retain 
the Na2O value for possible normative nepheline. 
9) Anorthite (An): 
a) If CaO is more than Al2O3, then subtract Al2O3 from CaO. Put all Al2O3 into anorthite. 
Al2O3 is now zero. 
b) If Al2O3 is more than CaO, then subtract CaO from Al2O3. Put all CaO into anorthite. CaO 
is now zero. 
Universidade de São Paulo Instituto de Geociências 
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10) Corundum (Cor): If Al2O3 is not zero, put the remaining Al2O3 into Corundum. Diopside 
and Al2O3 are now zero. 
11) Calculate the current ratio of Mg/(Mg+Fe+2). This ratio is called Mg' and will be the 
Mg/(Mg+Fe+2) ratio for all normative silicates. 
Mg' = MgO/(MgO+FeO) 
12) Calculate the mean formula weight of the remaining FeO and MgO. This combined Fe-
Mg oxide called FMO will be used in subsequent calculations. 
Formula weight of FMO = (Mg'*40.3044)+((1-Mg')*71.8464) 
13) Add FeO and MgO to get FMO. 
14) Diopside (Di): If CaO is not zero, subtract CaO from FMO. Put all CaO into diopside. 
CaO is now zero. 
15) Hypersthene (Hy) [Provisional]: Put all remaining FMO into hypersthene. Retain the 
FMO value for the possible calculation of normative olivine. 
16) Calculate the amount of SiO2 needed for all of the normative silicate minerals listed 
above, allotting SiO2 as follows: 
Orthoclase * 6 = needed SiO2 for each Orthoclase 
Albite * 6 = needed SiO2 for each Albite 
Anorthite * 2 = needed SiO2 for each Anorthite 
Diopside * 2 = needed SiO2 for each Diopside 
Hypersthene * 1 = needed SiO2 for each Hypersthene 
Sum the five SiO2 values just calculated, and call this number pSi for provisional SiO2. 
17) Quartz (Qz): If there is enough silica to make all five minerals then the rock is quartz-
normative. Otherwise there is no quartz in the norm and silica to make the rest of the 
silicates must come from other sources. 
Universidade de São Paulo Instituto de Geociências 
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São Paulo – 2006 Estêvão Inácio Sumburane 
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a) If pSi calculated in step 16 is less than SiO2, then there is excess silica. Subtract pSi 
from SiO2, and put excess SiO2 in quartz. SiO2, Nepheline, and olivine are now zero. Skip 
to step 20. 
b) If pSi calculated in step 16 is more than SiO2, then the rock is silica deficient. Proceed to 
step 18. 
18) Olivine (Ol), Hypersthene (Hy): If pSi calculated in step 16 is more than SiO2, then there 
is an SiO2 deficit. Quartz is now zero. Calculate a new pSi as in step 16, omitting 
hypersthene. 
Orthoclase * 6 = needed SiO2 for each Orthoclase 
Albite * 6 = needed SiO2 for each Albite 
Anorthite * 2 = needed SiO2 for each Anorthite 
Diopside * 2 = needed SiO2 for each Diopside 
Sum the four SiO2 values just calculated to get a new value of pSi. Subtract the new 
pSi from SiO2 to get the amount of SiO2 available for olivine and hypersthene, called 
aSi. 
a) If FMO is greater than or equal to 2 times aSi, then put all FMO in olivine. FMO and 
hypersthene are now zero. Proceed to step 19. 
b) If FMO is less than 2 times aSi, then nepheline is zero. Calculate the amount of 
hypersthene and olivine as follows: 
Hypersthene = ((2 * aSi) - FMO) 
Olivine = (FMO - Hypersthene) 
Skip to step 20. 
19) Nepheline (Ne), Albite (Ab): If you reached this step, then turning hypersthene into 
olivine in step 18a did not yield enough silica to make Or, Ab, An, Di, and Ol. Calculate a 
new pSi value as in step 16, omitting hypersthene and albite. 
Orthoclase * 6 = needed SiO2 for each Orthoclase 
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Anorthite * 2 = needed SiO2 for each Anorthite 
Diopside * 2 = needed SiO2 for each Diopside 
Olivine * 0.5 = needed SiO2 for each Olivine 
Sum the three SiO2 values just calculated to get a new value of pSi. Subtract this pSi 
from SiO2 to get a new value of aSi, which is the amount of SiO2 available for albite 
and nepheline. 
Albite = (aSi-(2*Na2O))/4 
Nepheline = Na2O-Albite 
20) Multiply orthoclase, albite, and nepheline by two. Divide olivine by two. 
21) Calculate An', which is the Ca/(Ca+Na) ratio in normative plagioclase: 
An' = Anorthite/(Anorthite+Albite) 
22) Plagioclase (Plag): Add albite to anorthite to make plagioclase. Retain the albite value. 
23) Calculate the formula weight of plagioclase, using the An' value from step 21. 
Formula weight Plag = (An'*278.2093)+((1-An')*262.2230) 
24) Multiply all of the normative mineral values by their respective formula weights. The 
formula weight of FMO is from step 12. 
Qz 60.0843 SiO2 
Or 278.3315 KAlSi3O8 
Plag Calculated in step 23 (Ca,Na)(Al,Si)4O8 
Cor 101.9613 Al2O3 
Ne 142.0544 NaAlSiO4 
Di 176.2480 + formula weight of FMO Ca(Fe,Mg)Si2O6 
Hy 60.0843 + formula weight of FMO (Fe,Mg)SiO3 
Ol 60.0843 + (2 * formula weight of FMO) (Fe,Mg)2SiO4 
Mt 231.5386 Fe3O4 
Universidade de São Paulo Instituto de Geociências 
___________________________________________________________________________ 
 
São Paulo – 2006 Estêvão Inácio Sumburane 
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Ilm 151.7452 FeTiO3 
Ap 504.3125 Ca5(PO4)3F 
25) This is your weight norm. This would usually be published along with four other useful 
parameters: 
Total: The sum of all mineral weights in the norm, calculated in step 24. Within rounding 
error the Total should be the same as the original total of the weight % of the oxides 
from the chemical analysis. 
Mg'%: 100*Mg' From step 11. 
An'%: 100*An' from step 21. 
DI: The Differentiation Index of Thornton and Tuttle (1960). This is the weight ratio: 
(Qz+Or+Ab+Ne)/Total. Ab is albite from step 20 times 262.2230. 
26) The weight norm is the way norms are usually expressed. If you want to compare 
norms to modes (which are volume fractions) you should divide each normative mineral by 
its density and normalize the Total back to 100%. Mineral densities can be gotten from 
mineralogy texts, the CRC Handbook of Chemistry and Physics, or elsewhere. The density 
of plagioclase and the Fe-Mg silicates with intermediate solid solutions can be found in 
tables or figures in mineralogy texts, or equations derived from them. 
27) Remember that this Excel spreadsheet program can calculate norms for you.