Normality Calculator (equivalents per litre)

Background.

Older analytical methods are full of instructions such as "titrate with 0.1 N sodium hydroxide" or "prepare 0.5 N sulfuric acid". The N stands for normality: equivalents of reacting substance per litre of solution. For sodium hydroxide it changes nothing, because one mole supplies one hydroxide ion and 0.1 N is simply 0.1 mol/L. For sulfuric acid it halves the number you order. Each mole gives up two protons, so 0.5 N sulfuric acid is a 0.25 mol/L solution, and buying a bottle labelled 0.5 M would double the acid in every titration.

The multiplier is the equivalence factor z, and it belongs to the reaction rather than to the chemical. Sulfuric acid titrated through both protons has z = 2; stopped at the first endpoint, z = 1. Potassium permanganate takes up five electrons in acid but three near neutral, so a single 0.02 mol/L solution is 0.1 N for one method and 0.06 N for another. No formula can reveal which reaction you intend, so z is entered by hand in every mode, along with the molar mass of the exact compound on the balance.

That ambiguity is why NIST Special Publication 811 calls the term obsolete and asks for the concentration of a named entity instead — c[(1/2)H₂SO₄] = 0.5 mol/dm³ in place of 0.5 N — and why IUPAC's Green Book leaves normality out of its concentration table altogether. The arithmetic is untouched by the relabelling. Normality survives in pharmacopoeial volumetric solutions and water-analysis methods because it lets a titration be solved without any mole ratio: at the endpoint, equivalents of titrant equal equivalents of sample, whatever the two substances are. Every result here comes with the molarity beside the normality, so you can report whichever your audience expects.

What is normality calculator?

Normality, symbol N, is the number of equivalents of a solute per litre of solution, in eq/L. What counts as one equivalent depends on the reaction: one mole of hydrogen ions transferred in an acid–base reaction, one mole of electrons in a redox reaction, one mole of unit charge in a precipitation. If one mole of the compound supplies z equivalents in the reaction you are running, then N = z × c, where c is the ordinary molarity, and the equivalent weight — the mass that supplies a single equivalent — is the molar mass divided by z. Because z is a whole number of at least 1 in the reactions met in practice, normality is never smaller than molarity, and the two are equal only when z = 1, as for hydrochloric acid, sodium hydroxide or thiosulfate in an iodine titration. NIST's formal version of the same idea counts a fractional entity: if a solution holds 0.25 mol of H₂SO₄ per litre, it holds 0.5 mol of (1/2)H₂SO₄ per litre, and that second figure is exactly the normality.

How to use this calculator.

1. 01Work out z before touching the calculator. Write the balanced equation or half-equation for your reaction and count what one mole of the solute supplies: HCl 1; H₂SO₄ 2, or 1 if you stop at the first endpoint; NaOH 1; Ca(OH)₂ 2; Na₂CO₃ 2 to the methyl-orange endpoint but 1 to phenolphthalein; KMnO₄ 5 in acid and 3 near neutral; K₂Cr₂O₇ 6.
2. 02Enter the molar mass of the exact formula you weigh, water of crystallisation included. The default, 98.072 g/mol, is sulfuric acid from the 2021 standard atomic weights; supplier labels often print 98.08 from an older sulfur value.
3. 03Choose the mode that matches your question: Normality when you have a molarity, Molarity when a method specifies a normality, Normality from a mass for a solution you made up, or the titration mode for an unknown.
4. 04Enter every volume in litres. 25.00 mL is 0.02500 L and 21.20 mL is 0.02120 L. The titration mode ignores the solution-volume field and uses the aliquot volume instead.
5. 05Copy the molarity into your notebook alongside the normality, or write the entity explicitly, such as c[(1/2)H₂SO₄] — either form tells the next reader which reaction the number assumed.

The formula.

Six relations cover every mode. Normality from molarity: N = z × c. Equivalent weight: EW = M ÷ z. Equivalents in a weighed mass: eq = m ÷ EW. Normality of a made-up solution: N = eq ÷ V. Mass for a given normality and volume: m = N × V × EW. And at a titration endpoint: N₁V₁ = N₂V₂.

The first line is a definition. NIST SP 811 gives the counting rule behind it: the amount of (1/x)B is x times the amount of B, so if 5 mol of H₂SO₄ is present, 15 mol of (1/3)H₂SO₄ is present. Applied per litre, the concentration of (1/z)B is z × c(B), which is N = z × c with the entity named.

The endpoint relation needs no separate assumption. An equivalent of acid is defined as the amount that reacts with one equivalent of base, so at the equivalence point the counts on both sides are equal by construction. Normality times volume turns each concentration into a count of equivalents; setting the two counts equal gives N₁V₁ = N₂V₂, with no stoichiometric coefficient anywhere. With molarities the same calculation needs the mole ratio from the balanced equation as an extra factor, and that factor is exactly what z has absorbed.

The equivalent weight is carried at full precision into every mass. Rounding 49.036 g/eq to 49.04 before multiplying would turn 24.518 g into 24.520 g, a 2 mg difference that a four-place analytical balance displays plainly.

Normality is per litre of solution, so it shares molarity's temperature dependence. Water expands by roughly 0.02 to 0.03 percent per degree Celsius near room temperature, and a dilute solution's normality falls by about that much as it warms, because the equivalents stay put while the volume grows. Volumetric glassware is calibrated at 20 °C for this reason.

z and the molar mass must be greater than zero, as must any volume that is divided by or used to report a mass. A normality or mass of exactly zero is accepted and simply returns zeros.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST Special Publication 811, 2008 edition, 'Guide for the Use of the International System of Units (SI)', section 8.6.5 note 2: 'The term normality and the symbol N should no longer be used because they are obsolete. One should avoid writing, for example, "a 0.5 N solution of H2SO4" and write instead "a solution having an amount-of-substance concentration of c[(1/2)H2SO4] = 0.5 mol/dm3".' This is the worked example reproduced on this page. Retrieved 2026-07-29.
2. [2]NIST Special Publication 811, 2008 edition, section 8.6.1 note 2: 'In general, n(xB) = n(B)/x, where x is a number. Thus, for example, if the amount of substance of H2SO4 is 5 mol, the amount of substance of (1/3)H2SO4 is 15 mol: n[(1/3)H2SO4] = 3n(H2SO4).' This is the identity c[(1/z)B] = z·c(B) that makes N = z·c formal. Retrieved 2026-07-29.
3. [3]BIPM, 'The International System of Units (SI)', 9th edition, 2019, section 2.3.1 (definition of the mole): 'The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.' Appendix 1 reproduces 14th CGPM (1971) Resolution 3 clause 2: 'When the mole is used, the elementary entities must be specified.' Consulted as an authority independent of NIST and IUPAC; it agrees. Retrieved 2026-07-29.
4. [4]IUPAC, 'Quantities, Units and Symbols in Physical Chemistry' (Green Book), 3rd edition, 2nd printing 2012, section 2.10, composition-of-mixtures table. Searched for 'normality', 'equivalent concentration' and 'equivalent entity': no occurrences. IUPAC does not endorse or explicitly deprecate normality in this table — it lists amount concentration c_B = n_B/V and omits normality entirely. Recorded here as documented silence rather than agreement. Retrieved 2026-07-29.
5. [5]IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Standard Atomic Weights 2021, abridged values. Used to build the molar masses printed on this page: H 1.008, S 32.06, O 15.999 giving M(H2SO4) = 98.072 g/mol; K 39.098, Mn 54.938, O 15.999 giving M(KMnO4) = 158.032 g/mol. Supplier labels often print 98.08 for sulfuric acid, derived from an older sulfur value. Retrieved 2026-07-29.
6. [6]NIST Special Publication 811, 2008 edition, front-matter check list item (18): 'The obsolete term normality and the symbol N, and the obsolete term molarity and the symbol M, are not used, but the quantity amount-of-substance concentration of B ... and its symbol cB and SI unit mol/m3 ... are used instead.' Confirms the deprecation is editorial policy for the whole document, not a footnote. Retrieved 2026-07-29.