Titration Calculator
Find the unknown molarity or volume in an acid-base titration from the equivalence-point condition, with stoichiometry (n_acid, n_base) for polyprotic acids and bases. A live 3D burette/flask animation and charts show the endpoint colour change and titration curve.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter any three of the four fields above and leave the unknown blank — it solves live. Volumes can be in mL or L as long as V_acid and V_base use the same unit.
Two ideas that trip students up
1. The flask stays clear, then flips colour fast
The left flask shows the solution before the equivalence point — clear. The right flask shows the same setup right at the endpoint — a phenolphthalein indicator turns pink almost the instant enough titrant has been added.
2. The titration curve is a steep S-shape, not a straight line
pH barely moves for most of the titration, then jumps sharply right at the equivalence volume, then flattens out again. That steep middle section is exactly where a good indicator needs to change colour.
Titration graphs
How it works
The core idea in one line: at the equivalence point, the acid and base have reacted in exactly the ratio the chemistry demands — moles of H⁺ delivered equal moles of OH⁻ delivered, which is what M_acid×V_acid×n_acid = M_base×V_base×n_base captures.
Macid × Vacid × nacid = Mbase × Vbase × nbase
equivalence-point condition
Macid × Vacid = Mbase × Vbase
simplified 1:1 case, nacid = nbase = 1
n = moles of H⁺ or OH⁻ per formula unit
e.g. n = 2 for H₂SO₄ or Ca(OH)₂
Rearranged, the same equation solves any one of the four quantities from the other three: Macid = (MbaseVbasenbase)/(Vacidnacid), and similarly for Vacid, Mbase or Vbase. In practice you never see the equivalence point directly — you watch for the endpoint, the volume at which an indicator changes colour, and use that volume as your best estimate of the true equivalence volume.
Worked example 1 — standardising an unknown HCl solution
Given: 25.00 mL of an unknown HCl solution is titrated with 0.100 M NaOH. The phenolphthalein endpoint is reached after 22.4 mL of NaOH is added. Both are monoprotic/monobasic (n_acid = n_base = 1). Find the HCl molarity.
The units of volume cancel as long as both are in the same unit (mL here), so V_acid and V_base do not need to be converted to litres first.
Worked example 2 — a diprotic acid (H₂SO₄) with NaOH
Given: 25.00 mL of an unknown H₂SO₄ solution is titrated with 0.200 M NaOH. The endpoint is reached after 30.0 mL of NaOH. H₂SO₄ supplies 2 H⁺ per molecule (n_acid = 2); NaOH supplies 1 OH⁻ (n_base = 1). Find the H₂SO₄ molarity.
Forgetting n_acid = 2 here would give the wrong answer (0.240 M) — double the true molarity — because each H₂SO₄ molecule neutralises two OH⁻, so fewer moles of acid are needed to match the same moles of base equivalents.
Common acid-base indicators and their colour-change ranges
Approximate standard transition (pH) ranges — pick an indicator whose range brackets the expected equivalence pH.
| Indicator | pH range | Colour change |
|---|---|---|
| Methyl orange | ≈ 3.1 – 4.4 | Red → yellow |
| Litmus | ≈ 5.0 – 8.0 (~7 midpoint) | Red → blue |
| Phenolphthalein | ≈ 8.2 – 10.0 | Colourless → pink |
Phenolphthalein (colourless→pink) is the classic choice for strong acid/strong base titrations because the equivalence point sits near pH 7, inside its steep transition window; methyl orange suits titrations with a lower equivalence pH.
Where titration actually matters
🔬 Laboratory quality control
Titration is a routine QC check for the concentration of acids, bases and other reagents on the shelf — labs re-standardise stock solutions regularly because concentrations drift with evaporation and handling.
🍋 Food & beverage acidity testing
The acidity of wine, juice, vinegar and dairy products is measured by titrating a sample against a standard base, reporting results as "percent acid" (e.g. percent citric or tartaric acid) — a key quality and flavour metric.
💧 Water hardness & alkalinity testing
Municipal and industrial water testing uses titration to measure alkalinity (acid-neutralising capacity) and hardness, guiding treatment decisions like lime dosing or ion-exchange softening.
💊 Pharmaceutical assay
Drug manufacturers titrate active ingredients to confirm a tablet or solution contains the labelled dose within tolerance — a required step in pharmacopeial quality assurance.
Common misconceptions
"The equivalence point and the endpoint are exactly the same thing."
The equivalence point is the true stoichiometric point defined by the reaction chemistry; the endpoint is the experimental signal (indicator colour change) used to approximate it. A well-chosen indicator makes the difference tiny, but they are conceptually distinct — the endpoint is always an estimate of the equivalence point.
"Any indicator works for any titration."
The indicator's colour-change pH range must bracket the pH at the equivalence point, or the visible endpoint will be noticeably off from the true equivalence point. Strong acid/strong base titrations (equivalence near pH 7) suit phenolphthalein or litmus; titrations with a more acidic equivalence point suit methyl orange.
"M1V1 = M2V2 always applies directly."
That simple form only holds when the acid and base react 1:1. For a diprotic acid like H₂SO₄ or a base like Ca(OH)₂ that supplies two reactive units per formula unit, you need the stoichiometric multipliers: M_acid × V_acid × n_acid = M_base × V_base × n_base.
"The titration curve's steep jump happens exactly at pH 7."
It happens at the equivalence point, which is only pH 7 for a strong acid vs strong base titration. Titrating a weak acid with a strong base gives an equivalence point above pH 7 (basic), and a weak base with a strong acid gives one below pH 7 (acidic), because the salt formed is not neutral.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — acid-base titrations and indicators (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 4, Aqueous Reactions and Solution Stoichiometry (acid-base titrations).
- • Skoog, West & Holler, Fundamentals of Analytical Chemistry — titrimetric methods and indicator selection.
M_acid × V_acid × n_acid = M_base × V_base × n_base at the equivalence point; n = 1 for simple monoprotic/monobasic reactions. The titration curve shown is a stylised illustrative sigmoid, not a rigorous equilibrium calculation. Results are rounded for display.
How to use this calculator
Set n_acid and n_base
Leave both at 1 for simple monoprotic/monobasic reactions, or change them for polyprotic acids and multi-hydroxide bases.
Enter three values
Fill any three of M_acid, V_acid, M_base, V_base; the fourth solves live.
Watch the endpoint
Use the titrant-volume slider to see the flask colour shift near the equivalence volume and watch the titration curve.
Related tools
Frequently asked questions
What is titration?
Titration is a lab technique for finding an unknown concentration by slowly adding a solution of known concentration (the titrant) from a burette into a measured volume of the unknown (the analyte) until the reaction is exactly complete. The volume of titrant used at that point lets you calculate the unknown concentration.
What is the equivalence point, and how is it different from the endpoint?
The equivalence point is the exact stoichiometric point where moles of acid and base (adjusted for their reacting ratio) are equal — a theoretical point defined by the chemistry. The endpoint is the point where an indicator visibly changes colour, which is what you actually observe during the experiment. A well-chosen indicator changes colour very close to the equivalence point, but the two are not identical by definition.
Why use an indicator at all?
An indicator is a weak acid or base whose two forms have different colours, and it changes colour over a narrow pH range. Because the pH jumps sharply near the equivalence point (see the titration curve below), a well-matched indicator flips colour right around that jump, giving a visible signal for a point you cannot see directly.
What does M_acid x V_acid = M_base x V_base assume?
This simplified 1:1 form assumes the acid and base react in a 1:1 mole ratio (one H+ neutralised per one OH-), which holds for monoprotic acids like HCl reacting with monobasic bases like NaOH. For polyprotic acids (like H2SO4, which supplies 2 H+) or multi-hydroxide bases (like Ca(OH)2), you must include the stoichiometric multipliers n_acid and n_base: M_acid x V_acid x n_acid = M_base x V_base x n_base.
Is the titration curve on this page a real pH calculation?
No — it is a stylised, illustrative S-shaped (sigmoid) curve centred on the equivalence volume, meant to show the characteristic shape (a slow drift, then a steep jump, then another slow drift) rather than compute real pH from equilibrium constants. A rigorous curve requires the acid/base Ka or Kb, initial concentrations, and a full equilibrium calculation at every point — well beyond a simple ratio calculator.