What formula does this titration calculator use?

It uses the standard equivalence-point relationship C_a × V_a / n_a = C_t × V_t / n_t, where C is concentration in mol/L, V is volume in mL, and n is the stoichiometric coefficient from the balanced equation. At the equivalence point the moles of analyte neutralised exactly equal the moles of titrant delivered (adjusted for stoichiometry), so this equation holds exactly.

What is the mole ratio (n_a and n_t)?

These come from the balanced chemical equation. For a 1:1 reaction such as HCl + NaOH → NaCl + H_2O both are 1. For H_2SO_4 + 2 NaOH → Na_2SO_4 + 2 H_2O, n_a = 1 and n_t = 2 (two moles of NaOH react per mole of sulfuric acid). Entering the wrong ratio is the most common source of error in titration calculations.

How do I find the concentration of an unknown acid?

Select "Analyte concentration (C_a)" as the unknown. Enter the volume of acid you placed in the flask (V_a), the concentration of your NaOH standard solution (C_t), and the volume of NaOH used to reach the endpoint (V_t). The calculator applies C_a = C_t × V_t × n_a / (V_a × n_t) and shows the molarity of the acid.

Can this calculator handle diprotic or triprotic acids?

Yes. For a diprotic acid such as H_2SO_4 titrated with NaOH to both equivalence points, set n_a = 1 and n_t = 2 (for the second equivalence point). For a triprotic acid like H_3PO_4 reaching its third equivalence point, use n_a = 1, n_t = 3. The formula scales linearly with the mole ratio.

What units should I use?

Enter all concentrations in mol/L (molar, M) and all volumes in millilitres (mL). The calculator converts volumes to litres internally for the mole calculation, so the displayed result is always back in mol/L or mL as appropriate.

Does this work for redox and precipitation titrations too?

Yes. The equivalence-point formula is general — it applies to any titration where you have a known stoichiometric ratio between titrant and analyte. For a permanganate–oxalate redox titration (5 moles oxalate per 2 moles permanganate) set n_a = 5 and n_t = 2. For precipitation titrations, set the mole ratio from the balanced ionic equation in the same way.

Titration Calculator

Titration is one of the most precise quantitative techniques in analytical chemistry — a measured volume of a standard solution (titrant) of known concentration is gradually added to a solution of unknown concentration (analyte) until the reaction reaches its equivalence point. By recording exactly how much titrant was delivered, you can back-calculate the exact amount of analyte present. This calculator automates that calculation for any acid–base, redox, or precipitation titration where you know three of the four key values and the stoichiometric mole ratio from the balanced equation.

The equivalence-point formula

At the equivalence point the moles of analyte neutralised exactly equal the moles of titrant delivered, scaled by the stoichiometric ratio from the balanced equation:

C_a × V_a / n_a = C_t × V_t / n_t

Symbol	Meaning	Typical unit
C_a	Concentration of analyte	mol/L (M)
V_a	Volume of analyte (flask)	mL
n_a	Stoichiometric coefficient of analyte	dimensionless
C_t	Concentration of titrant (standard)	mol/L (M)
V_t	Volume of titrant delivered at endpoint	mL
n_t	Stoichiometric coefficient of titrant	dimensionless

Rearranging for each unknown:

C_a = (C_t × V_t × n_a) / (V_a × n_t)
V_t = (C_a × V_a × n_t) / (C_t × n_a)
C_t = (C_a × V_a × n_t) / (V_t × n_a)
V_a = (C_t × V_t × n_a) / (C_a × n_t)

The calculator applies whichever rearrangement matches your chosen unknown and displays the full working line so you can check every step.

How it works

Select the unknown — choose which of the four quantities you need to find.
Enter the stoichiometric mole ratio — read n_a and n_t from the balanced equation (both = 1 for a simple 1:1 neutralisation such as HCl + NaOH).
Fill in the three knowns — concentrations in mol/L, volumes in mL.
Read the result — the answer updates instantly along with derived quantities: moles of analyte, moles of titrant delivered, and equivalents.

All arithmetic is done in your browser; nothing is uploaded anywhere.

Worked example — finding the concentration of acetic acid in vinegar

A student pipettes 25.00 mL of vinegar into a conical flask and adds phenolphthalein indicator. They titrate with a 0.1000 mol/L NaOH standard solution. The endpoint (pale pink, persistent for 30 s) is reached after 18.35 mL of NaOH has been added.

Balanced equation: CH₃COOH + NaOH → CH₃COONa + H₂O (1:1 ratio, n_a = 1, n_t = 1).

C_a = (0.1000 × 18.35 × 1) / (25.00 × 1) = 0.07340 mol/L

Vinegar is typically 4–8% acetic acid by mass, which corresponds to roughly 0.7–1.3 mol/L — this result (0.0734 mol/L) would suggest a very dilute sample or a calculation error worth checking, which is exactly the kind of sanity-check a good tool should prompt.

Second example — H₂SO₄ + NaOH (2:1 ratio): 25.00 mL of 0.0500 mol/L H₂SO₄ titrated with 0.1000 mol/L NaOH to the second equivalence point. How much NaOH is needed?

n_a = 1, n_t = 2 (two OH⁻ per SO₄²⁻):

V_t = (0.0500 × 25.00 × 2) / (0.1000 × 1) = 25.00 mL

This 1:1 volume ratio makes intuitive sense because the NaOH is exactly twice as concentrated as the sulfuric acid but needs two moles per mole of acid.

Formula note

The calculator uses the analytical equivalence-point formula, which is exact for any stoichiometric titration. It does not model buffer curves, pH gradients, or indicator transition ranges — those require full acid–base equilibrium treatment. For routine stoichiometry problems (A-level, IB, first-year university) this formula is the standard and correct approach.