The titration calculator above works out an unknown concentration from a measured titre, or the titrant volume that a known analyte would consume at the equivalence point. It handles acid-base titrations at any stoichiometry and redox titrations where you supply the ratio from the balanced half-equations. Every intermediate value is printed — moles of titrant, moles of analyte, equivalence volume and the mass in the aliquot — so the final number can be checked step by step rather than accepted whole.
Arb Digital builds free calculators that expose their working. A titration result is a chain of four small operations, and an error anywhere in the chain produces a plausible-looking answer. Showing the moles at each stage makes a wrong mole ratio or a stray millilitre visible immediately, which a single output number never does.
What This Titration Calculator Does
In its default mode it converts the titre into moles of titrant, applies the mole ratio from the balanced equation to get moles of analyte, and divides by the aliquot volume to give the unknown concentration. A second mode reverses this to predict the equivalence volume for a known analyte, which is what you use when planning a run so you know roughly where the end point should fall. A third mode solves for the titrant concentration, which is the standardisation calculation you perform against a primary standard.
The reaction type selector sets the two coefficients for the common acid-base cases and then gets out of the way. For a redox titration you enter the ratio directly, because it depends on the electrons transferred in the specific half-reactions rather than on any general rule.
The optional molar mass box converts moles of analyte into a mass, which is how you report the amount of a substance in a sample rather than its concentration — the usual output of a purity determination.
A boundary worth stating: the molarity calculator derives a concentration from a weighed mass and a volume. This page derives one from a reaction with a standard solution. It is the same quantity reached by an entirely different route, and the titration route is what you use when the substance cannot be weighed accurately in pure form.
How to Use It
- Balance the reaction first and read off the coefficients of the analyte and the titrant. The selector sets these for common acid-base cases.
- Enter the titrant concentration from the label if it is a standardised solution, or from a standardisation titration if you made it yourself.
- Enter the mean titre in millilitres, using concordant runs only and discarding the rough one.
- Enter the aliquot volume that was in the conical flask, which is the pipetted portion and not the total volume of your sample.
- Check the moles line in the grid. Moles of titrant and moles of analyte should differ by exactly your mole ratio, which is a fast sanity check on the coefficients.
The Formula and How It Is Calculated
At the equivalence point the two reagents have been mixed in exactly the ratio the balanced equation demands. For a reaction written aA + bB, that condition is n(A) / a = n(B) / b, where n is amount in moles. Since n = C × V with volume in litres, the working form is CAVA / a = CBVB / b, and rearranging for the unknown analyte concentration gives CA = (a / b) × CBVB / VA.
Taking the defaults: 25.00 mL of 0.100 mol/L sodium hydroxide is 0.02500 L × 0.100 = 2.500 × 10⁻³ mol. In a one-to-one reaction that neutralises 2.500 × 10⁻³ mol of hydrochloric acid, and dividing by the 20.00 mL aliquot, or 0.02000 L, gives 0.1250 mol/L. Change the analyte to sulfuric acid and the ratio becomes one acid to two base, halving the answer to 0.0625 mol/L from the same titre. The equilibrium constants that determine indicator choice, discussed below, are the 25 degree values in the University of Massachusetts chemistry ionisation constant tables.
The Equivalence Point Is Not Always pH 7
Equivalence means stoichiometric equivalence: the exact amount of titrant needed to react with all the analyte. Whether that leaves a neutral solution depends entirely on what is left behind, and only one of the four common cases gives pH 7.
A strong acid titrated with a strong base leaves a salt of a strong acid and a strong base, which does not hydrolyse, so the equivalence point sits at pH 7 — a value that follows from the IUPAC Gold Book definition of pH and the ion product of water rather than from anything about the titration itself. A weak acid titrated with a strong base leaves the conjugate base of that weak acid, which is itself basic, so the equivalence point lands above 7 — commonly near 8.7 for acetic acid at ordinary concentrations. A weak base titrated with a strong acid leaves a conjugate acid and lands below 7. A weak acid titrated with a weak base has such a shallow inflection that a visual indicator is not usable at all.
This is why indicator choice is not arbitrary. Phenolphthalein changes colour around pH 8.3 to 10, which suits a weak acid against a strong base and is wrong for a weak base against a strong acid. Methyl orange changes around 3.1 to 4.4, which is the reverse. Using the wrong one shifts the apparent end point away from the true equivalence point and biases every result in the same direction, which is exactly the kind of error that repeating the titration will never reveal. The pH calculator lets you check where the equivalence point should actually fall for a given weak acid.
The Half-Equivalence Point and Why It Is Useful
Halfway to equivalence in a weak acid titration, exactly half the acid has been converted to its conjugate base, so the two are present in equal amounts. Put that one-to-one ratio into the buffer equation and the logarithm term vanishes, leaving pH = pKa.
That gives a direct experimental route to a pKa with no extra apparatus: titrate the acid, find the volume at equivalence, go back to half that volume and read the pH there. It is also the most strongly buffered point of the whole curve, which is why the plot is flattest in that region and why titration curves are the standard way of demonstrating buffer behaviour. The Henderson-Hasselbalch calculator is built on the same relationship.
For a polyprotic acid, each dissociation produces its own equivalence point and its own half-equivalence point, provided the pKa values are far enough apart. Phosphoric acid shows two clear inflections in practice and a third that is too shallow to see, because the final pKa is so high that water competes.
Redox Titrations Use Electrons, Not Protons
The mole ratio in a redox titration comes from balancing electrons between the two half-reactions, and it is frequently not one to one. Permanganate in acid gains five electrons per ion as it is reduced to manganese, while iron in the plus-two state loses one electron each, so one permanganate reacts with five iron ions. Entering a one-to-one ratio here would make the answer wrong by a factor of five.
The convention that trips people up is which species the coefficients describe. This calculator asks for the analyte coefficient and the titrant coefficient as they appear in the balanced overall equation. For permanganate titrating iron, the analyte is iron with a coefficient of 5 and the titrant is permanganate with a coefficient of 1.
Some redox titrations are self-indicating, permanganate being the classic example: the first excess drop turns the solution permanently pink because the reagent itself is intensely coloured. Others use a specific indicator such as starch for iodine. Either way the arithmetic on this page is unchanged; only the ratio differs.
Where a Titration Result Comes From and Goes
Upstream, the titrant has to be standardised, which is itself a titration against a primary standard — a substance stable and pure enough to be weighed directly. Preparing that standard uses the molarity calculator and a molar mass from the molar mass calculator. If the titrant was made from a concentrated stock, the solution dilution calculator gives the volumes.
Downstream, a titration result is often converted to a mass or a percentage purity, which needs the moles to grams calculator, and compared against an accepted value with the percent error calculator. Where the reaction is a synthesis rather than an analysis, the percent yield calculator takes over.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Assuming a one-to-one mole ratio — a diprotic acid consumes twice the base, and a permanganate titration is one to five.
- Using the total sample volume instead of the aliquot — only the pipetted portion in the flask reacted with the titrant.
- Including the rough titre in the mean — the first run overshoots by design and belongs outside the average.
- Choosing an indicator by habit — the equivalence point of a weak acid against a strong base is well above pH 7, so a low-range indicator biases every result.
- Confusing end point with equivalence point — one is what the indicator shows, the other is where the stoichiometry balances, and the gap between them is a systematic error.
Related Free Tools From Arb Digital
Prepare and standardise solutions with the molarity calculator and the solution dilution calculator, get molar masses from the molar mass calculator, and predict where a weak-acid equivalence point falls with the pH calculator. The chemical equation balancer supplies the coefficients this page depends on, and the full free online tools hub lists everything else.
Frequently Asked Questions
Convert the titre to moles by multiplying concentration by volume in litres, apply the mole ratio from the balanced equation to get moles of analyte, then divide by the aliquot volume in litres. The calculator shows each of those three steps.
It is the point at which exactly enough titrant has been added to react with all the analyte according to the balanced equation. It is defined by stoichiometry, not by a particular pH, and it is not observed directly but inferred from an indicator or a probe.
No. It is pH 7 only for a strong acid against a strong base. A weak acid titrated with a strong base leaves a basic conjugate and finishes above 7, while a weak base against a strong acid finishes below 7.
The equivalence point is where the stoichiometry balances. The end point is where the indicator changes colour. A well-chosen indicator puts the two close together, and the small remaining gap is a systematic error known as indicator error.
Balance the two half-equations so the electrons lost equal the electrons gained, then read the coefficients from the combined equation. Permanganate gains five electrons and iron in the plus-two state loses one, giving a one to five ratio.
Half the weak acid has been converted to its conjugate base, so the two are present in equal amounts. The logarithm term in the buffer equation becomes zero and the pH equals the pKa, which is a direct experimental route to that constant.
The rough run is performed quickly to locate the approximate end point and usually overshoots. Only the subsequent runs, added dropwise near the expected volume and agreeing within a small tolerance, are averaged into the reported titre.
This calculator is provided for education and general reference. It describes how titration arithmetic works and is not laboratory, safety or handling guidance; follow the procedures and risk assessments issued by your own institution.
