Our Titration Calculator finds the unknown concentration of a solution (analyte) from your acid-base titration data. Enter the known titrant volume and concentration, the analyte volume, and the stoichiometric mole ratio to get the result instantly.
Titration Calculator
Titration Formula
At the equivalence point: n₁V₁ = n₂V₂
Where n = mole ratio coefficient, V = volume × concentration (in mol).
Rearranged: C_analyte = (V_titrant × C_titrant) / (ratio × V_analyte)
Example: 24.5 mL of 0.1 M NaOH neutralises 25.0 mL of HCl (1:1 ratio):
C(HCl) = (0.0245 × 0.1) / (1 × 0.025) = 0.098 mol/L
Steps in an Acid-Base Titration
- Fill the burette with the titrant (known concentration solution)
- Pipette a fixed volume of the analyte (unknown solution) into a conical flask
- Add a few drops of indicator (phenolphthalein for strong acid/base)
- Add titrant slowly until the indicator changes colour (endpoint)
- Record the volume used and calculate using the formula above
- Repeat at least 3 times and take the average titre
Common Titration Indicators
| Indicator | pH Range | Best For |
|---|---|---|
| Phenolphthalein | 8.3 – 10.0 | Strong acid + strong base |
| Methyl orange | 3.1 – 4.4 | Strong base + weak acid |
| Litmus | 5.0 – 8.0 | General-purpose |
| Bromothymol blue | 6.0 – 7.6 | Near-neutral equivalence points |
Worked Example
Standard titration calculations use the relationship:
25.00 mL of an unknown HCl solution is titrated with 0.100 M NaOH, and the endpoint is reached at 22.40 mL:
- M1 x 25.00 = 0.100 x 22.40
- M1 = (0.100 x 22.40) / 25.00
- M1 = 0.0896 M HCl
For a reaction where the mole ratio is not 1:1, add the ratio into the equation: M1V1 / a = M2V2 / b, where a and b are the stoichiometric coefficients of the acid and base in the balanced equation.
Worked example with a 1:2 ratio
Titrating H2SO4 (diprotic, reacts 1:2 with NaOH) using 20.00 mL of unknown acid against 0.150 M NaOH, endpoint at 18.60 mL:
- M1 x 20.00 / 1 = 0.150 x 18.60 / 2
- M1 x 20.00 = 1.395
- M1 = 0.0698 M H2SO4
Forgetting the factor of 2 for a diprotic acid is one of the most common titration calculation errors.
Endpoint vs Equivalence Point
These terms are often used loosely but describe different things.
| Term | Definition |
|---|---|
| Equivalence point | The theoretical point where moles of acid exactly equal moles of base, calculated from stoichiometry |
| Endpoint | The point you actually observe, usually a colour change in the indicator |
A well-chosen indicator changes colour very close to the true equivalence point, so the small gap between the two, called the titration error, is negligible for most purposes. A poorly chosen indicator can introduce a meaningful systematic error.
Why Titrations Are Run in Triplicate
- Detecting outliers. A single run cannot tell you whether a result is reliable. Three runs let you spot one that is clearly off.
- Improving precision. Averaging concordant results, defined as titres within 0.10 mL of each other, reduces the impact of small reading errors.
- Standard laboratory practice. Most protocols require reporting the mean of concordant titres rather than a single value.
Choosing an Indicator
| Titration type | Suitable indicator | Colour change |
|---|---|---|
| Strong acid, strong base | Phenolphthalein or methyl orange | Colourless to pink, or red to yellow |
| Weak acid, strong base | Phenolphthalein | Colourless to pink |
| Strong acid, weak base | Methyl orange | Red to yellow |
| Weak acid, weak base | Difficult, no sharp endpoint; use a pH meter instead | – |
The rule of thumb is that the indicator’s colour-change range should sit as close as possible to the pH at the true equivalence point, which itself depends on whether the titration involves strong or weak reagents.
Common Titration Mistakes
- Forgetting the stoichiometric ratio for reactions that are not 1:1, such as diprotic or triprotic acids.
- Reading the burette from the wrong angle. Read at eye level, at the bottom of the meniscus.
- Overshooting the endpoint. Add titrant dropwise and swirl constantly as you approach the expected volume.
- Not rinsing the burette with the titrant before filling, which dilutes the first readings.
- Averaging a discordant result into the mean, which quietly corrupts an otherwise reliable set of data.
Frequently Asked Questions
What is the formula for titration calculations?
For a 1:1 acid-base reaction, M1V1 = M2V2, where M is molarity and V is volume. If the mole ratio is not 1:1, such as with a diprotic acid, include the stoichiometric coefficients: M1V1/a = M2V2/b. Forgetting that ratio for something like sulfuric acid, which reacts 1:2 with a monoprotic base, is a very common source of error.
What is the difference between endpoint and equivalence point?
The equivalence point is the theoretical moment when moles of acid exactly equal moles of base, calculated from stoichiometry. The endpoint is what you actually observe during the titration, typically an indicator colour change. A well-chosen indicator changes colour very close to the true equivalence point, so the difference between the two is usually negligible.
Why do we do 3 titrations?
To check for outliers and improve precision. A single titration cannot tell you whether the result is reliable, while three runs let you identify concordant results, typically defined as titres within 0.10 mL of each other, and average those. Any titre that falls well outside that range is treated as an outlier and excluded rather than averaged in.
Which indicator should I use for acid-base titration?
It depends on the strength of the acid and base involved. Phenolphthalein suits titrations ending in a basic solution, such as a weak acid with a strong base. Methyl orange suits titrations ending in an acidic solution, such as a strong acid with a weak base. Either works for strong acid with strong base. Weak acid with weak base has no sharp colour-change endpoint, so a pH meter is used instead.
What does it mean for titres to be concordant?
Concordant titres are results from repeated titrations that agree closely with each other, conventionally within 0.10 mL. Only concordant results are averaged to calculate the final titre. A result that falls well outside that range is discarded as an outlier rather than included in the average, since it would otherwise skew an accurate result.
How do I calculate molarity from a titration?
Once you have the volume of titrant used at the endpoint, apply M1V1 = M2V2 (adjusted for stoichiometry if the ratio is not 1:1) using the known molarity and volume of your standard solution. For example, 25.00 mL of unknown HCl titrated to endpoint with 22.40 mL of 0.100 M NaOH gives an HCl concentration of 0.0896 M.
What causes titration errors?
Common causes include overshooting the endpoint by adding titrant too quickly, misreading the burette meniscus from the wrong eye level, not rinsing the burette with the titrant before filling so the first reading is diluted, using an indicator whose colour-change range does not match the equivalence point pH, and averaging a discordant outlier into the final result instead of discarding it.