Titration Calculator (unknown concentration)

Understanding the titration calculator — concept and principle

In a titration you add a solution of known concentration (the titrant) to a measured volume of an unknown solution (the analyte) until the reaction is exactly complete, as shown by an indicator colour change or a pH or potential jump. This calculator turns the titrant volume read from the burette into the concentration of the analyte, and also gives the moles of titrant used.

Moles delivered from the burette equal moles in the flask at the end point: 2.45 mmol in 25 mL is 0.098 M.

How it is calculated

C_a = C_t × V_t × r ÷ V_a

C_t: titrant concentration (M); V_t: titrant volume at the endpoint (mL).
V_a: analyte volume (mL). Because V_t and V_a are both in mL, the units cancel.
r: mole ratio analyte : titrant from the balanced equation (moles of analyte per mole of titrant).
Moles of titrant = C_t × V_t ÷ 1000.

The principle

At the equivalence point the moles of titrant added and the moles of analyte present are in the exact ratio of the balanced equation. Moles of titrant are C_t × V_t; multiplying by r gives moles of analyte; dividing by the analyte volume gives its concentration. For HCl + NaOH the ratio is 1, for H₂SO₄ titrated with NaOH it is 0.5 (one H₂SO₄ uses two NaOH). The endpoint you observe should be as close as possible to this equivalence point, which is why the indicator must change colour at the right pH.

Worked example

Defaults: C_t = 0.1 M, V_t = 24.5 mL, V_a = 25 mL, r = 1.

Moles of titrant: 0.1 × 24.5 ÷ 1000 = 0.00245 mol.
Moles of analyte: 0.00245 × 1 = 0.00245 mol.
Concentration: 0.1 × 24.5 × 1 ÷ 25 = 0.098 M.

Each point is the calculator re-run with only “Analyte volume (mL)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Analyte volume (mL)	Analyte concentration (M)
6.25	0.392
12.5	0.196
18.8	0.1306666667
25	0.098
31.2	0.0784
37.5	0.0653333333
50	0.049

How to read the result

The analyte is slightly less concentrated than the titrant because less than 25 mL of titrant was needed. Repeat the titration until two or three results agree closely (often within 0.1 mL in a teaching lab) and average them. A titrant volume in the middle of the burette's range gives the best relative precision.

Common mistakes

Using the wrong mole ratio, especially for diprotic acids or redox titrations such as permanganate.
Reading the burette at the top of the meniscus or from an angle (parallax).
Using the first rough titration in the average.
Not standardising the titrant; NaOH solutions absorb CO₂ and change concentration.

Keep in mind: The result is only as good as the titrant concentration, glassware calibration and endpoint detection. For regulated analyses follow the validated method and its uncertainty budget.

Frequently asked questions

What mole ratio do I use for H₂SO₄ titrated with NaOH?

r = 0.5, because H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O.

What is the difference between endpoint and equivalence point?

The equivalence point is the theoretical stoichiometric point; the endpoint is where your indicator or instrument signals it.

Which indicator should I use?

One whose colour-change range includes the pH at equivalence, for example phenolphthalein for a weak acid titrated with a strong base.

Sources: Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman · Skoog, D. A., West, D. M., Holler, F. J., Crouch, S. R., Fundamentals of Analytical Chemistry, Cengage

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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