About the Titration Calculator
This titration calculator does the stoichiometry behind an acid–base, redox or precipitation titration. In concentration mode, enter the titrant molarity, the volume of titrant delivered at the end point and the volume of analyte you pipetted, and it returns the analyte concentration. In equivalence-point mode, enter a known (or estimated) analyte concentration and it tells you how much titrant you will need — handy for choosing the right burette size or titrant strength before you start.
A mole-ratio field handles reactions that are not 1:1, such as sodium hydroxide reacting with sulfuric acid (2 mol NaOH per mol H₂SO₄) or permanganate oxidising iron(II) (1 mol MnO₄⁻ per 5 mol Fe²⁺). Add the analyte molar mass if you also want the result in grams per litre.
For strong acid–strong base titrations the calculator also draws the theoretical pH curve, assuming a monoprotic titrant such as NaOH or HCl, complete dissociation and 25 °C (Kw = 1.0 × 10⁻¹⁴). Weak acids and bases have a buffer region and a shifted equivalence pH that this simple curve does not model, but the concentration result is valid for any titration with known stoichiometry.
How to use the titration calculator
- 1Choose whether you want the unknown concentration or the titrant volume at equivalence.
- 2Enter the titrant molarity and the analyte volume you pipetted.
- 3Enter the burette volume at the end point (or the known analyte concentration).
- 4Set the mole ratio from the balanced equation — 1 for HCl + NaOH.
- 5Optionally add the analyte molar mass and pick a pH curve type.
Formula and method
At the equivalence point the moles of titrant added are exactly the amount the balanced equation requires for the analyte. Moles of titrant = Cₜ × Vₜ. Dividing by the mole ratio r (mol titrant per mol analyte) gives moles of analyte, and dividing that by the analyte volume gives its concentration. Volumes can stay in millilitres because the units cancel; only the moles output converts mL to L.
For a 1:1 reaction this collapses to the familiar M₁V₁ = M₂V₂. The pH curve treats both acid and base as fully dissociated and solves [H⁺] from the leftover acid or base, including water autoionization (Kw = 10⁻¹⁴), so it passes smoothly through pH 7 at equivalence.
- Cₜ, Vₜ
- Titrant concentration (mol/L) and volume delivered (mL)
- Cₐ, Vₐ
- Analyte concentration (mol/L) and volume (mL)
- r
- Mole ratio: mol titrant per mol analyte from the balanced equation
Worked examples
HCl standardised with 0.1 M NaOH
21.5 mL of 0.100 M NaOH contains 2.15 mmol of hydroxide, which neutralised 2.15 mmol of HCl in a 25.0 mL aliquot. Concentration = 2.15 ÷ 25.0 = 0.0860 M, or 0.0860 × 36.46 = 3.14 g/L.
Sulfuric acid needs 2 mol NaOH per mol
18.4 mL of 0.200 M NaOH is 3.68 mmol. Because H₂SO₄ is diprotic, that neutralises 3.68 ÷ 2 = 1.84 mmol of acid in 20.0 mL, so [H₂SO₄] = 0.0920 M.
Planning a titration: volume to equivalence
A 10.0 mL sample at about 0.12 M contains 1.2 mmol of analyte. With 0.050 M titrant at a 1:1 ratio you need 1.2 ÷ 0.050 = 24.0 mL — comfortably inside a 50 mL burette.
Frequently asked questions
How do you calculate concentration from a titration?+
Multiply the titrant molarity by the volume used (in litres) to get moles of titrant, convert to moles of analyte with the mole ratio from the balanced equation, then divide by the analyte volume in litres.
What is the difference between the end point and the equivalence point?+
The equivalence point is where stoichiometrically equal amounts have reacted. The end point is where the indicator changes colour. A well-chosen indicator makes the end point fall within a drop or two of the equivalence point.
Can I use M1V1 = M2V2 for titrations?+
Only when the reaction is 1:1, such as HCl with NaOH. For H₂SO₄ with NaOH, or most redox titrations, include the mole ratio or you will be off by a factor of 2, 5 or more.
What pH is the equivalence point?+
For a strong acid with a strong base it is pH 7 at 25 °C. For a weak acid titrated with a strong base it is above 7, and for a weak base with a strong acid it is below 7, because the conjugate ion hydrolyses.
How many titrations should I run?+
Run a rough titration first, then repeat accurate titrations until at least two titres agree within about 0.10 mL, and average the concordant values before calculating.