Titration Calculator

Imagine filling a bathtub with colored dye until the water turns exactly neutral gray. You know how much dye you started with and how much clear water you added. From those two facts, you can calculate either the strength of the dye or the volume of water needed. Titration works the same way: you add a solution of known concentration (the titrant) to a solution of unknown concentration until the reaction is exactly complete — the equivalence point, usually marked by an indicator color change.

The math behind it is conservation of moles. At the equivalence point, the moles of acid equal the moles of base. Since moles = molarity x volume, you get M1 x V1 = M2 x V2. This is exact for monoprotic acid-monobase pairs. The elegance is that it does not matter what the chemicals are — only their concentrations and the volumes matter.

The equivalence point is not the same as the endpoint. The endpoint is where the indicator changes color, which is slightly past the true equivalence point. In careful lab work, that small overshoot (called the titration error) is corrected using a blank titration or a more precise indicator. For most educational and practical purposes, the two are treated as identical.

Use this calculator any time you have an acid-base neutralization with a known 1:1 molar ratio and three of the four variables. Common situations: determining the concentration of a freshly prepared solution, verifying a stock solution has not degraded, calculating how much titrant a procedure will consume, or working backward from a known result to infer what volume was used.

Do not use this calculator when the stoichiometry is not 1:1 (polyprotic acids, polybasic bases, or redox titrations with complex ratios). Do not use it when you are estimating concentration from a partial titration — only equivalence point data belongs here. Complexometric titrations (EDTA, for example) and precipitation titrations follow different equilibrium logic and may appear to fit M1V1 = M2V2 only by coincidence in dilute systems.

This calculator also assumes the reaction goes to completion. If your system involves a weak acid and a weak base where equilibrium lies well short of completion, the equivalence point calculation requires a more detailed treatment involving Ka and Kb. In practice, most bench titrations use a strong acid or strong base on at least one side, which drives the reaction to completion.

The most frequent mistake is confusing volume units. Entering liters instead of milliliters makes the result 1,000x too large, and entering microliters makes it 1,000x too small. The calculator expects mL throughout. If your burette reads in mL (as most do), you are already in the right unit.

A second common error is using the final burette reading instead of the delivered volume. The delivered volume is final reading minus initial reading. If you start at 1.25 mL and end at 19.75 mL, you delivered 18.50 mL — not 19.75 mL. Using the raw final reading systematically overestimates V2 and underestimates the calculated concentration.

The third mistake is applying this formula to polyprotic reactions without adjusting for stoichiometry. Titrating H2SO4 against NaOH with a 1:2 ratio and entering raw molarities will give an answer that is off by a factor of 2. Whenever your balanced equation has coefficients other than 1:1, you must divide one molarity by its coefficient before using this calculator.

The fundamental equation is M1V1 = M2V2, where M is molarity in mol/L and V is volume in any consistent unit (milliliters work fine since the units cancel). Rearranging gives you whichever unknown you need:

Solving for unknown concentration: M2 = (M1 x V1) / V2 Solving for unknown volume: V2 = (M1 x V1) / M2

Moles at equivalence: moles = M x V(L) = M x V(mL) / 1000. This number is the same for both solutions at equivalence, which is why it serves as the check that your inputs are consistent.

For reactions with molar ratios other than 1:1, the equation becomes M1V1/n1 = M2V2/n2, where n is the stoichiometric coefficient. For H2SO4 + 2NaOH, n1 = 1 and n2 = 2, so you divide the NaOH moles by 2. This calculator handles only n1 = n2 = 1. When your reaction ratio differs, adjust your input molarity by the ratio factor before entering it.

M1V1 = M2V2 assumes that the stoichiometric n-factor is 1 for both species. Where it quietly breaks down is in non-aqueous titrations, where activity coefficients diverge significantly from 1 and the effective concentration driving the equilibrium is not the same as the analytical molarity you measure gravimetrically. In highly concentrated solutions (above roughly 1 M), ion pairing reduces effective molarity below nominal molarity, meaning the true equivalence point arrives before the formula predicts. In environmental monitoring, matrix effects from dissolved salts can shift indicator endpoints by 0.1 to 0.3 pH units, introducing systematic error that algebraic manipulation cannot correct.