Titration Calculator
At the equivalence point of an acid-base titration, the reactive protons from the acid exactly match those neutralised by the base. Enter the three known quantities and the proton counts to find the fourth. Optionally choose a titration type to also calculate the pH at equivalence, the half-equivalence pH, and the best indicator to use.
Formula
Worked example
A 25.0 mL sample of acetic acid (weak acid, pKa 4.76, nₐ = 1) is titrated to equivalence with 22.0 mL of 0.100 mol/L NaOH (n_b = 1). Acid concentration: Mₐ = (1 x 0.100 x 22.0) / (1 x 25.0) = 0.088 mol/L. Total volume at equivalence = 47.0 mL, so cSalt = 0.0022 mol / 0.047 L = 0.0468 mol/L. Equivalence pH = 7 + 0.5 x (4.76 + log 0.0468) = 7 + 0.5 x (4.76 - 1.33) = 8.72, which is basic, consistent with the conjugate base (acetate) hydrolysing in water. The half-equivalence pH = pKa = 4.76, where the solution is a perfect buffer.
The equivalence-point equation
A titration determines an unknown concentration or volume by reacting a solution of known properties against it until the reaction is exactly complete, the equivalence point. For an acid-base titration, completeness means every reactive proton the acid can donate has been neutralised by the base. Mathematically that gives nₐ x Mₐ x Vₐ = n_b x M_b x V_b, where M is molarity, V is volume, and n is the number of transferable protons per molecule. Rearranging this single equation lets you solve for whichever one of the four bulk quantities you did not measure, which is exactly what this calculator does. Volumes can be in millilitres or litres provided both acid and base volumes share the same unit, since they appear only as a ratio.
pH at the equivalence point
The equivalence-point pH depends on the strength of the acid and base used. A strong acid neutralised by a strong base produces a salt that does not hydrolyse, so the pH at equivalence is exactly 7.00 at 25 degrees C. A weak acid titrated by a strong base produces a conjugate base that is a weak base itself; it accepts a proton from water and raises the pH above 7. The approximate equivalence-point pH is 7 + 0.5*(pKa + log cSalt), where cSalt is the concentration of conjugate base in the mixed solution. Conversely, a strong acid titrated by a weak base forms a conjugate acid that lowers the pH below 7, with the formula 7 - 0.5*(pKb + log cSalt). Knowing the equivalence pH before you start tells you exactly which indicator to choose.
Half-equivalence point and the buffer region
When exactly half the required titrant has been added in a weak acid titration, the concentrations of the weak acid and its conjugate base are equal. The Henderson-Hasselbalch equation then simplifies to pH = pKa. This is the half-equivalence point. It sits at the midpoint of the flat buffer region of the titration curve, where the pH changes only slowly with added titrant. Knowing the half-equivalence pH is useful in two practical ways: it tells you the pKa of an unknown acid from a simple half-volume reading, and it confirms you are in the buffer region if you need a stable pH for a reaction.
Choosing the right indicator
An acid-base indicator is a weak acid whose conjugate base has a different colour. It changes colour over roughly a 2-pH-unit range centred on its own pKa. The indicator must change colour at the equivalence pH, not just any pH. For a strong acid-strong base titration at pH 7, bromothymol blue (range 6.0-7.6) or phenol red (6.8-8.4) are ideal. For a weak acid-strong base titration with an equivalence pH near 8.5-9, phenolphthalein (8.2-10.0) is the classic choice. For a strong acid-weak base titration with an equivalence pH near 5, methyl orange (3.1-4.4) or methyl red (4.4-6.2) works well. Using the wrong indicator can introduce a systematic error of several percent in the measured concentration.
Equivalence point versus endpoint
The equivalence point this calculator computes is a theoretical quantity, the exact stoichiometric match of acid and base. In the lab you detect it through an endpoint, usually a colour change from an indicator or a sharp jump on a pH curve. The two coincide only when the indicator changes colour at the equivalence pH. For a strong acid-strong base system the jump in the titration curve is so steep (several pH units per tiny drop of titrant) that almost any indicator near pH 7 works. For weak acid or weak base systems the jump is less dramatic and indicator choice matters more. Using a pH meter to track the full titration curve and locate the inflection point removes the indicator ambiguity entirely.
Common titration species: proton counts and strength
| Species | Formula | Type | n | pKa / pKb |
|---|---|---|---|---|
| Hydrochloric acid | HCl | Strong acid | 1 | N/A (strong) |
| Nitric acid | HNO₃ | Strong acid | 1 | N/A (strong) |
| Sulfuric acid | H₂SO₄ | Strong diprotic | 2 | N/A (1st); 1.99 (2nd) |
| Phosphoric acid | H₃PO₄ | Weak triprotic | 3 | 2.15 / 7.20 / 12.35 |
| Acetic acid | CH₃COOH | Weak acid | 1 | 4.76 |
| Formic acid | HCOOH | Weak acid | 1 | 3.75 |
| Hydrofluoric acid | HF | Weak acid | 1 | 3.17 |
| Oxalic acid | H₂C₂O₄ | Weak diprotic | 2 | 1.25 / 4.27 |
| Sodium hydroxide | NaOH | Strong base | 1 | N/A (strong) |
| Potassium hydroxide | KOH | Strong base | 1 | N/A (strong) |
| Calcium hydroxide | Ca(OH)₂ | Strong diacidic | 2 | N/A (strong) |
| Ammonia | NH₃ | Weak base | 1 | pKb 4.74 |
| Methylamine | CH₃NH₂ | Weak base | 1 | pKb 3.36 |
| Pyridine | C₅H₅N | Weak base | 1 | pKb 8.77 |
For polyprotic species titrated to a partial equivalence point, set n to the protons reacted up to that step. pKa values at 25 degrees C.
Frequently asked questions
What units should I use for the volumes?
Choose millilitres or litres from the unit selector next to each volume field. Both sides must use the same unit for the ratio to cancel. The equivalents output always shows moles (mol), converting volumes to litres internally.
Why is the equivalence-point pH not always 7?
pH 7 only applies when a strong acid is neutralised by a strong base, because the resulting salt (such as NaCl) does not hydrolyse. When a weak acid is titrated by a strong base, the conjugate base (such as acetate) is itself a weak base and raises the pH above 7. When a strong acid is titrated by a weak base, the conjugate acid lowers the pH below 7. The calculator accounts for this using the approximate formula pH = 7 +/- 0.5*(pKa or pKb + log cSalt).
What is the half-equivalence point and why does it matter?
The half-equivalence point is reached when exactly half the stoichiometric amount of titrant has been added. At this point, for a weak acid titration, the concentrations of the weak acid and its conjugate base are equal, so the Henderson-Hasselbalch equation gives pH = pKa. This makes it a simple experimental method for measuring pKa: just read the pH when the burette reading is half the equivalence volume. It also marks the centre of the buffer region, where pH is most stable.
How do I handle a diprotic acid like sulfuric acid?
Set the acid proton count nₐ to 2 for H₂SO₄ titrated to its full equivalence point, because each mole donates two protons. The calculator then correctly accounts for the fact that one mole neutralises two moles of a monoacidic base such as NaOH. If you are titrating only to the first equivalence point of a polyprotic acid, set n = 1.
How do I choose the right indicator?
The indicator recommendation updates automatically once you select a titration type. The calculator estimates the equivalence-point pH and suggests an indicator whose colour-change range brackets that pH. For a strong/strong titration (pH 7) bromothymol blue or phenol red work well. For a weak acid/strong base titration (pH typically 8-10) phenolphthalein is classic. For strong acid/weak base (pH typically 4-6) use methyl orange or methyl red.
Is the equivalence point the same as the endpoint?
No. The equivalence point is the exact stoichiometric match calculated here, while the endpoint is where your indicator changes colour or the pH meter shows a sharp jump. They coincide only when the indicator changes at the equivalence pH. For high accuracy, track the full pH curve and locate the inflection point, or choose your indicator carefully using the pH value this calculator provides.