Endpoint stoichiometry
CaVaνa = CtVtνt
M₁V₁ = M₂V₂ is valid only for a 1:1 equivalent relationship.
Acid–Base Titration Calculator
Calculator inputs
In automatic mode, leave analyte concentration or titrant volume blank.
Use positive concentrations and sample volume. A delivered volume of zero is valid for initial pH.
Advanced constants and stoichiometric coefficients
Required for supported weak-acid or weak-base pH calculations.
Use reactive equivalents from the balanced reaction. Curve calculations are limited to supported one-step systems.
Result summary
Answer
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Enter values and calculate.
Current point
pH: —
Region: —
Neutralized: —
Endpoint
Equivalence volume: —
Equivalence pH: —
Remaining: —
Indicator guidance
Transition range: —
Suitable indicators: —
Stoichiometry
Analyte: —
Titrant added: —
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An indicator endpoint is an observed approximation of the stoichiometric equivalence point. Instrumental detection is preferable when no transition range fits the steep part of the curve.
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Interactive titration curve
pH versus added titrant volume from zero to twice the equivalence volume.
InitialBuffer regionHalf-equivalenceEquivalenceInspected point
Accessible curve data table
| Point | Titrant volume | pH | Region |
|---|
Calculation steps
- Enter values and calculate to see unit conversions, mole balance, the applicable formula, substituted values, and the rounded answer.
Mole-balance table
| Species or quantity | Amount | Formal concentration | Role |
|---|---|---|---|
| Calculate to populate the balance. | |||
How to use the calculator
- Choose the requested unknown, or leave it on automatic detection and leave that value blank.
- Select a reaction preset or set the analyte/titrant type and balanced-reaction equivalents.
- Enter molarity and volumes. For an unknown analyte concentration, the delivered volume must be the endpoint titre.
- For a weak analyte pH or curve, enter its Ka, pKa, Kb, or pKb, then calculate.
Titration formula reference
Molarity C is amount per solution volume (mol L−1); moles n are found from n = CV. Volumes must be in litres when calculating moles. In the equations below, Va is analyte volume, Vt is titrant volume, and νa/νt are reactive acid/base equivalents.
Initial weak solution
Ka = [H+][A−]/[HA]
For an initial weak base, use Kb and solve for [OH−]. The calculator uses the quadratic/equilibrium balance, not the small-x shortcut.
Strong-species excess
[H+] − Kw/[H+] = (acid equivalents − base equivalents)/Vtotal
This water-inclusive balance is used before or after equivalence for strong systems.
Weak buffer region
pH = pKa + log10(nA−/nHA)
At half-equivalence, nA− = nHA, so pH = pKa. Mole ratios may replace concentration ratios because both species share the same total volume.
Weak-system equivalence
Kb = Kw/Ka (conjugate base); Ka = Kw/Kb (conjugate acid)
Conjugate-species hydrolysis shifts equivalence pH away from 7.
Charge-balance curve model
The calculator numerically solves mass balance, electroneutrality, and Kw = [H+][OH−] at every supported curve point. This removes the discontinuous Henderson–Hasselbalch switch near zero addition and equivalence.
Model scope: ideal aqueous solutions at 25 °C; Kw = 1.0 × 10−14. Activities, ionic strength, dilution heat, mixed solvents, precipitation, redox chemistry, and multi-step polyprotic equilibria are not modelled. pH is not forcibly restricted to 0–14 because concentrated ideal solutions can have formal values outside that interval.
Complete worked examples
Unknown HCl molarity
25.00 mL HCl requires 20.00 mL of 0.1000 M NaOH. For 1:1 stoichiometry, Ca = (0.1000 × 0.02000)/0.02500 = 0.08000 M.
Required volume, non-1:1
10.00 mL of 0.1000 M H₃PO₄ needs three OH− equivalents per mole. VNaOH = (0.1000 × 0.01000 × 3)/0.1500 = 20.00 mL.
Weak-acid pH before equivalence
For 25.00 mL of 0.1000 M acetic acid (pKa 4.76) plus 10.00 mL of 0.1000 M NaOH, the charge-balance result is pH 4.585.
Weak-acid equivalence pH
With the same acetic acid and 25.00 mL NaOH, acetate hydrolysis gives pH 8.730 at equivalence.
pH after equivalence
At 30.00 mL NaOH, 0.000500 mol OH− remains in 0.05500 L, giving pH 11.959.
Practical titration checks
Read the burette correctly
Record initial and final readings at eye level. Delivered titre = final reading − initial reading; it is not automatically the final reading.
Use concordant titres
Repeat until your method's agreement criterion is met, then average only the accepted concordant titres. Do not silently include a rough trial.
Apply blanks consistently
Subtract or otherwise apply a validated reagent blank according to the method before calculating analyte concentration.
Check coefficients and units
Balance the reaction before using molarity-volume relationships, and convert both volumes consistently. Coefficients matter whenever the equivalent ratio is not 1:1.
Endpoint is an estimate
The observed colour change approximates equivalence. Add titrant dropwise near the endpoint and use instrumental detection when the pH jump is unsuitable.
Choose the correct mode
Use unknown concentration for a measured endpoint titre, equivalence volume for the theoretical endpoint, and pH mode only for a supported equilibrium system.
Method, review status, and sources
Author: Starlight Tools editorial teamUpdated: Independent chemistry reviewer: not claimed
The endpoint solver uses balanced acid/base equivalents. Supported pH curves are calculated with numerical charge and mass balances, including water autoionization, instead of switching abruptly between textbook approximations. Results were checked against standard strong/strong and acetic-acid benchmark values.
Titration calculator FAQ
How do I calculate an unknown molarity from a titration?
At equivalence, use CaVa·na = CtVt·nt and rearrange to Ca = CtVt·nt/(Va·na). Convert both volumes to the same unit first.
When is M1V1 = M2V2 valid?
Only when the reacting acid and base have a 1:1 equivalent relationship. Otherwise include the balanced-reaction coefficients or acid/base equivalents.
How do stoichiometric coefficients change the titration equation?
Multiply each molarity-volume term by the number of reactive acid or base equivalents: CaVa·na = CtVt·nt. For H2SO4 neutralized completely by NaOH, na = 2 and nt = 1.
What is the difference between endpoint and equivalence point?
The equivalence point is the exact stoichiometric completion point. The endpoint is the observed indicator or instrument response and only approximates equivalence.
How do I find delivered burette volume?
Delivered titre equals final burette reading minus initial burette reading. Apply any validated blank correction consistently before using the titre.
How should I choose an acid-base indicator?
Choose an indicator whose full transition range lies within the steep pH change around equivalence. Use a pH meter or another instrumental method when no common range fits well.
How many significant figures should a titration answer have?
Report the final concentration or volume to the precision supported by the least precise measured input, while keeping extra digits during intermediate calculations.
Why is weak-system equivalence pH not 7?
A weak acid leaves a basic conjugate base at equivalence, while a weak base leaves an acidic conjugate acid. Their hydrolysis shifts pH above or below 7.
How does temperature affect titration pH?
Temperature changes Kw and acid/base equilibrium constants, so neutral pH and the calculated curve can shift. This calculator fixes temperature at 25 °C and Kw = 1.0 × 10⁻¹⁴.
Can this calculator draw polyprotic titration curves?
No. Polyprotic presets are supported only for total-equivalent endpoint stoichiometry. Their multiple dissociation steps require additional constants and a more detailed equilibrium model.
Limits and lab note
Use this as a study aid or planning helper, not as a substitute for a validated analytical method. Real titrations can differ because of activities, calibration, temperature, dissolved carbon dioxide, ionic strength, and side reactions.