A titration measures an unknown concentration by adding a solution of known concentration, the titrant, until the reaction is just complete. Reading how much titrant that took gives the answer. This calculator handles the arithmetic for acid–base titrations with any mole ratio and also models what happens along the way: it computes the pH at every point, plots the titration curve, reports the pH at the start, the half-equivalence point and the equivalence point, and recommends an indicator.
How to use the titration calculator
- Choose what to Solve for: the analyte concentration (the usual unknown), the titrant volume needed, the analyte volume or the titrant concentration.
- Pick the Titration type: strong acid with strong base, weak acid with strong base, strong base with strong acid, or weak base with strong acid. For weak ones, enter the pKa or pKb.
- Set the Analyte coefficient and Titrant coefficient from the balanced equation (1 and 1 for most monoprotic acids and bases).
- Enter the known concentrations in M or mM and volumes in mL, L or µL. The titrant volume is the buret reading at the endpoint minus the starting reading.
- Read the result, the millimoles reacted, the key pH values, the suggested indicator, the curve and the table of pH at fractions of the equivalence volume.
Titration formula
At the equivalence point, with analyte coefficient a and titrant coefficient t:
For a 1:1 reaction this reduces to the familiar CaVa = CtVt. Volumes only need to share a unit, since they appear as a ratio. The pH curve is computed from the full charge balance of the mixture at each point, including water’s own ions, with Kw = 10−14 at 25 °C.
Worked example
Acetic acid in vinegar
A 25.00 mL sample of diluted vinegar needs 18.75 mL of 0.1000 M NaOH to reach the phenolphthalein endpoint. Acetic acid reacts 1:1 with NaOH.
Ca = 0.1000 M × 18.75 mL ÷ 25.00 mL = 0.07500 M (1.875 mmol of acid)
With pKa = 4.76, the pH starts at 2.95, passes 4.76 at 9.375 mL (half-equivalence) and reaches 8.70 at the equivalence point. The indicator suggestion is phenolphthalein, whose 8.2–10 range brackets 8.70.
A diprotic acid. Titrating 25.00 mL of sulfuric acid with 0.1000 M NaOH takes 18.75 mL. With coefficients 1 (H2SO4) and 2 (NaOH), the acid concentration is 0.1000 × 18.75 ÷ (2 × 25.00) = 0.03750 M, half of what a 1:1 calculation would suggest.
Shapes of titration curves
| Titration | Starting pH | pH at equivalence | Typical indicator |
|---|---|---|---|
| Strong acid + strong base | Low (about 1) | 7.00 | Bromothymol blue or phenolphthalein |
| Weak acid + strong base | About 3 | Above 7 | Phenolphthalein |
| Strong base + strong acid | High (about 13) | 7.00 | Bromothymol blue or methyl red |
| Weak base + strong acid | About 11 | Below 7 | Methyl red |
Near the equivalence point the pH changes by several units with a single drop of titrant, which is what makes the endpoint easy to see. Between about 10% and 90% of the way, a weak-acid curve is flat because the mixture is a buffer; the buffer pH calculator explains that region.
Getting good titration results
Rinse the buret with titrant first so water does not dilute it, read the bottom of the meniscus at eye level, swirl the flask continuously and add titrant dropwise near the endpoint. Doing three titrations that agree within 0.1 mL is standard practice. Standardize sodium hydroxide against a primary standard such as potassium hydrogen phthalate, because NaOH absorbs carbon dioxide and water from the air.
For preparing the titrant, see the molarity calculator and the dilution calculator; to convert any concentration to pH, use the pH calculator.
Frequently asked questions
How do I calculate the concentration from a titration?
At the equivalence point, moles of titrant times the analyte coefficient equal moles of analyte times the titrant coefficient. For a 1:1 reaction, Ca = Ct × Vt ÷ Va. If 18.75 mL of 0.1000 M NaOH neutralizes 25.00 mL of acid, the acid is 0.0750 M.
What are the coefficient fields for?
They hold the mole ratio from the balanced equation. Sulfuric acid reacts with sodium hydroxide as H₂SO₄ + 2NaOH, so enter 1 for the analyte and 2 for the titrant. Leaving both at 1 is right for HCl, HNO₃, acetic acid, NaOH and NH₃.
Why is the pH at the equivalence point not always 7?
Only for strong acid with strong base. When a weak acid is titrated, its conjugate base remains at the equivalence point and makes the solution basic, around pH 8.7 for 0.075 M acetic acid. A weak base gives an acidic equivalence point.
Which indicator should I use?
One whose color change brackets the equivalence pH. Phenolphthalein (8.2–10) suits weak acid–strong base titrations, methyl red (4.4–6.2) suits weak base–strong acid titrations, and bromothymol blue or phenolphthalein both work for strong–strong ones because the pH jumps so steeply.
Why does the pH at half-equivalence equal the pKa?
Halfway to the equivalence point, exactly half of the weak acid has been converted to its conjugate base, so their concentrations are equal and the Henderson–Hasselbalch equation gives pH = pKa. Chemists use this to measure pKa values.