Acid–Base Titration Calculator
Concentration from the endpoint, equivalence points, the pH curve and the right indicator.
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Result
Titration curve
pH against the volume of titrant added; dots mark the equivalence points and the half-equivalence points.
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About the Acid–Base Titration Calculator
Three jobs of an acid–base titration in one place. Work out the unknown concentration of a sample from the titrant volume at the endpoint — one reading or several trials with their mean and spread. Standardize your titrant from a weighed primary standard such as potassium hydrogen phthalate, sodium carbonate or borax. Or draw the full titration curve of a strong or weak, mono-, di- or triprotic acid or base and get every equivalence point, its pH, the half-equivalence points where pH ≈ pKa, and the indicators whose colour change falls on the steep part of the curve.
The curve is exact: the volume of titrant is worked out for every pH from the charge balance (the method of de Levie), with water and every proton counted, so it is right near the start, at the equivalence points and for very weak or very dilute acids, where the textbook shortcuts break down. The acid and base constants are those of the OpenStax Chemistry 2e tables, so textbook problems come out as in the book. Each endpoint is graded by how sharply the pH jumps around it, and each indicator by how close to the equivalence volume its colour changes.
With a Pro pass, copy the result or download the curve and the readings as a CSV, or unlock this one result. Without a pass the free preview shows the unknown concentration or the equivalence point in full, the first rows of each table, the first working step and a watermarked curve; other figures hidden.
How to use it
- Choose Curve and equivalence point, Unknown concentration or Standardize the titrant.
- Pick the sample (an acid, a base, or your own weak acid or base by its pKa values) and the titrant, then enter the volume of the sample and the concentration of the titrant.
- For the curve, enter the sample’s concentration; for an unknown, enter the titrant volume at the endpoint (several trials separated by commas) and which endpoint you reached; to standardize, enter the masses weighed and the volumes used.
- Read the result, the equivalence points with the size of their pH jump, the pH table, the indicators and the working.
- Copy the result or download it as a CSV — with a Pro pass, or after unlocking this result.
Examples
25.00 mL of 0.100 M CH₃COOH, 0.100 M NaOH
Equivalence at 25.00 mL and pH 8.72; half-way, at 12.50 mL, pH 4.75 ≈ pKa 4.74; phenolphthalein changes within 0.2 % of the equivalence volume
The same titration as OpenStax Chemistry 2e Table 14.2, reproduced to ±0.02 pH.
25.00 mL of sample, 0.100 M NaOH, endpoints 24.85, 24.90 and 24.80 mL
0.0994 M HCl, standard deviation 0.0002 M over three trials
0.5105 g of potassium hydrogen phthalate needs 24.85 mL
c(NaOH) = 0.5105 g ÷ 204.22 g/mol ÷ 0.02485 L = 0.1006 M
25.00 mL of 0.0500 M Na₂CO₃, 0.100 M HCl
Two equivalence points: 12.50 mL at pH 8.35 with no clear jump, and 25.00 mL at pH 3.99, where methyl orange works
25.00 mL of 0.100 M H₃PO₄, 0.100 M NaOH
25.00 mL at pH 4.70 (bromocresol green, to its intermediate colour), 50.00 mL at pH 9.67 (thymolphthalein); the third proton gives no endpoint
Common uses
- Chemistry lab reports: the concentration from your trials, with the mean and standard deviation
- Standardizing NaOH with KHP or HCl with sodium carbonate, borax or Tris before an analysis
- Predicting a titration before you run it: where the endpoint is, how sharp it is and which indicator to use
- Homework on titration curves of weak and polyprotic acids, with the exact curve and the working
Formulas
- Concentration from the endpoint: c(sample) = c(titrant) × V(titrant) × (mol of sample per mol of titrant) ÷ V(sample); for H₂SO₄ with NaOH the ratio is ½, for Na₂CO₃ with HCl to the second endpoint ½, for borax with HCl ½
- Standardization: c(titrant) = m × purity ÷ M × (mol of titrant per mol of standard) ÷ V(titrant)
- Equivalence volume: V = n(sample) × (mol of titrant per mol of sample) ÷ c(titrant), one for each proton the titrant takes or gives
- The curve: from the charge balance, V(titrant) = −(V₀·D + P) ÷ (D + c) for a base titrant and (V₀·D + P) ÷ (c − D) for an acid titrant, with D = [H⁺] − [OH⁻] and P the charge of the sample’s ions at that pH (de Levie): exact for an ideal solution
- Half-equivalence: where half of a proton is titrated, [HA] = [A⁻] and pH ≈ pKa — only approximately for stronger or dilute acids, where the acid’s own reaction with water shifts the amounts (the calculator shows the real pH)
Choosing an indicator
An indicator works when its whole colour change falls on the steep part of the curve. For each equivalence point the calculator finds the titrant volumes at which each indicator starts and finishes changing colour: Good when that happens within 0.5 % of the equivalence volume, Usable within 2 %, and Intermediate colour when only the colour half-way through the change is close enough. Where none fits, the pH jump is too small for an indicator: use a pH meter and take the steepest point of the curve.
Ranges used (approximate, as every source says): thymol blue 1.2–2.8 and 8.0–9.6, methyl orange 3.4–4.4, bromocresol green 3.8–5.4, methyl red 4.2–6.3, bromocresol purple 5.2–6.8, bromothymol blue 6.0–7.6, phenol red 6.8–8.4, cresol red 7.2–8.8, phenolphthalein 8.3–10.0, thymolphthalein 9.3–10.5, alizarin yellow R 10.1–12.0.
Sources
- OpenStax, Chemistry 2e, §14.7 Acid–Base Titrations, and its tables of Ka and Kb values (with Kw = 1.0 × 10⁻¹⁴)
- R. de Levie, Explicit expressions of the general form of the titration curve in terms of concentration, J. Chem. Educ. 70, 209
- D. Harvey, Analytical Chemistry 2.1, §9.2 Acid–Base Titrations/09%3A_Titrimetric_Methods/9.02%3A_AcidBase_Titrations): indicator ranges, with thymolphthalein’s from OpenStax Figure 14.19
- R. N. Goldberg, N. Kishore and R. M. Lennen, Thermodynamic Quantities for the Ionization Reactions of Buffers, NIST: the pKa values of potassium hydrogen phthalate and Tris
Limitations
- The curve is for an ideal solution at 25 °C (Kw = 1.0 × 10⁻¹⁴): activity effects, which shift measured pH values by a few hundredths to tenths at high ionic strength, are not included.
- Titrants are strong monoprotic acids or bases (HCl, HNO₃, HClO₄, NaOH, KOH); titrations with a weak titrant, redox, complexometric and precipitation titrations are not covered.
- Carbon dioxide absorbed from the air makes the carbonate endpoints and strong bases drift; boiling off CO₂ near the second carbonate endpoint sharpens it, which an ideal curve cannot show.
- Indicator ranges vary a little between sources and with the observer; treat the grades as a guide.
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Frequently asked questions
What do I get without a pass?
Without a pass, Acid–Base Titration Calculator shows the unknown concentration or the equivalence point in full, the first rows of each table, the first working step and a watermarked curve; other figures hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the concentration from a titration?
Multiply the titrant’s concentration by its volume at the endpoint to get the moles of titrant, convert to moles of sample with the balanced equation, and divide by the sample’s volume. For 25.00 mL of HCl needing 24.85 mL of 0.100 M NaOH: 0.100 × 0.02485 = 2.485 mmol, so c = 2.485 mmol ÷ 25.00 mL = 0.0994 M.
Why is the pH at the equivalence point not 7?
Only for a strong acid with a strong base. At the equivalence point of a weak acid only its conjugate base is left, which makes the solution basic: 8.72 for acetic acid with NaOH. A weak base titrated with a strong acid ends acidic: 5.28 for 0.1 M ammonia with HCl.
Why does pH equal pKa at the half-equivalence point?
When half the acid is neutralized, [HA] = [A⁻], so Henderson–Hasselbalch gives pH = pKa + log 1 = pKa. It is exact only when the acid is weak and not too dilute: for phosphoric acid’s first proton (pKa 2.12) the real pH there is 2.27, which the calculator shows.
Which indicator should I use?
One whose colour change falls on the steep part of the curve: phenolphthalein for a weak acid with a strong base, methyl red for a weak base with a strong acid, and almost any of methyl red, bromothymol blue or phenolphthalein for a strong acid with a strong base. The calculator grades each indicator for your own concentrations.
How do I standardize NaOH with KHP?
Weigh dry potassium hydrogen phthalate (204.22 g/mol), dissolve it and titrate to the phenolphthalein endpoint; one mole of KHP takes one mole of NaOH. 0.5105 g needing 24.85 mL gives 0.5105 ÷ 204.22 ÷ 0.02485 = 0.1006 M.
What if my acid is not in the list?
Choose “Another weak acid” or “Another weak base” and type its pKa values (one to three; for a base, those of its conjugate acid). The curve, the equivalence points and the indicators are worked out the same way.