Titration Calculator
M_a·V_a·n_a = M_b·V_b·n_b at the equivalence point: the unknown concentration, the titrant volume, moles and normality, and a sample’s percent purity.
The concentration or volume you solved for, millimoles and equivalents on each side, normality for polyprotic acids and bases, the mass of analyte at your molar mass, and the sample’s percent purity.
Example: 25 mL of an acid needing 22.4 mL of 0.1 M NaOH is 0.0896 M (2.24 mmol). With H₂SO₄ (n = 2) the same 0.05 M in 25 mL takes twice the titrant: 25 mL of 0.1 M base.
Equivalents on one side
match equivalents on the other.
The balance at the equivalence point, what n means, and why the end point is a different thing.
The balance
At the equivalence point exactly enough titrant has been added to react with all the analyte: M_a·V_a·n_a = M_b·V_b·n_b. The n on each side is the number of reacting units per formula unit — protons for an acid or base, electrons for a redox titration, ligands for a complexometric one. HCl and NaOH are 1; H₂SO₄ and Ca(OH)₂ are 2, so 25 mL of 0.05 M sulfuric acid needs twice the sodium hydroxide that 25 mL of 0.05 M hydrochloric would. Multiplying molarity by n gives normality, in which the balance is simply N_a·V_a = N_b·V_b.
What you can solve
Any one of the four quantities: the unknown concentration in the flask (the usual case), the volume of titrant a known analyte will need (planning the burette), or the titrant concentration from a titration against a primary standard (standardising). With a molar mass the moles become a mass, and with the mass you actually weighed out, a percent purity — the number an assay is usually reported as. A purity above 100 % means something is wrong with the molar mass, the equivalence factor or the weighing, and the page says so rather than printing it flat.
Equivalence is not the end point
The equivalence point is stoichiometric — it exists whether or not you can see it. The end point is where your indicator changes colour or the meter jumps, and the small gap between them is the titration error, reduced by choosing an indicator whose range brackets the equivalence pH and by running a blank. No indicator table, no titration curve and no pH at the equivalence point are computed here: those depend on the strengths of the acid and base, which is the pH tool's job. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- M_a·V_a·n_a = M_b·V_b·n_b at the equivalence point, n being the protons or electrons exchanged per formula unit; normality N = M × n; the end point is not the equivalence point
Last reviewed 22 September 2026. How results are checked: How we verify.