Titration Calculator

The titration calculator is a free, browser-based acid-base titration solver that handles every common bench scenario: a strong acid + strong base standardisation (HCl + NaOH), a weak acid + strong base endpoint (acetic acid + NaOH), a strong acid + weak base back-titration (HCl + NH₃), and a polyprotic titration (H₂SO₄, H₃PO₄, H₂CO₃, oxalic acid). For any of these you can leave one of the four fields blank, titrant molarity, titrant volume, analyte molarity, or analyte volume, and the calculator solves the conservation equation M_a · V_a · n_a = M_b · V_b · n_b for the unknown you have left blank. Coefficients are the stoichiometric ratios of the reaction (1:1 for HCl + NaOH, 2:1 for H₂SO₄ + 2NaOH, 3:1 for H₃PO₄ + 3NaOH). The result panel reports the moles of acid and base reacted, the pH at the equivalence point (7.00 for strong-strong, or from salt hydrolysis for weak-strong and strong-weak), the pH at the half-equivalence point via Henderson-Hasselbalch (for weak + strong), and the indicator recommendation ranked against the CRC Handbook of Chemistry and Physics (102nd ed., Section 8) table.

The underlying stoichiometry is the same conservation of acidic and basic equivalents that governs every wet-lab titration: at the equivalence point, the moles of H⁺ delivered by the acid equal the moles of OH⁻ delivered by the base, scaled by the number of protons each species donates or accepts. The calculator also reports equivalence pH so the user can pick an indicator whose transition range brackets the jump. The Henderson-Hasselbalch result at half-equivalence is a useful sanity check and is a standard teaching point in undergraduate analytical chemistry (Harris, Quantitative Chemical Analysis, 10th ed., Ch. 16). The indicator table is the standard CRC list, phenolphthalein (8.0 to 10.0), bromothymol blue (6.0 to 7.6), methyl orange (3.1 to 4.4), litmus (5.0 to 8.0), phenol red (6.8 to 8.2), and thymol blue (8.0 to 9.6), and the recommendation picks the indicator whose transition midpoint is closest to the computed pH_eq.

The calculator runs entirely in the browser; none of the inputs are stored, transmitted, or associated with any account. Inputs and outputs are accurate to about 15 significant digits of IEEE-754 double-precision floating-point resolution, which is well below the precision of any volumetric flask or analytical balance. Real-world accuracy is limited by the purity of the standard reagent, the volumetric accuracy of the burette and pipette, and the temperature control of the working solution; the calculator reports values at the formal 25 °C reference temperature with pKw = 14.00.

How to use this calculator

1. Pick a mode from the four button row: Strong + strong, Weak + strong, Strong + weak, or Polyprotic. The mode controls the pH-equivalence calculation and the available presets (weak-acid list, weak-base list, polyprotic acid list).
2. Enter the four known fields: titrant molarity (M_b), titrant volume (V_b), analyte molarity (M_a), and analyte volume (V_a). Leave the field you want to solve blank, the calculator will detect the empty field and return the corresponding value.
3. For weak + strong and strong + weak modes, choose the weak-acid or weak-base preset from the dropdown (or type the pKa / pKb directly). The pH at equivalence depends on the salt hydrolysis constant, so the pKa value is required.
4. For polyprotic mode, pick the polyprotic acid from the dropdown (H₂SO₄, H₃PO₄, H₂CO₃, oxalic acid). The stoichiometry ratio auto-fills to the number of acidic protons (2 for diprotic, 3 for triprotic).
5. Click the Solve for dropdown to explicitly choose which field is the unknown (V_b, M_b, V_a, M_a, or ratio). The calculator blanks the chosen field so the display is consistent.
6. Read the Result panel: the solved value with units, the moles of acid and base reacted, the pH at the equivalence point, the pH at the second equivalence point (for triprotic acids), the titrant volume at the equivalence point, and the half-equivalence titrant volume (weak + strong only).
7. Read the Indicator recommendation table: indicators ranked by the absolute difference between their transition pH and pH_eq. The smallest ΔpH is highlighted as the best match.
8. Use the Quick test cases buttons to load the five canonical examples (HCl + NaOH, acetic + NaOH, unknown analyte concentration, H₂SO₄ + NaOH, HCl + NH₃) and verify the math by hand.
9. All results are live, change any input and the result panel updates immediately. There is no "Calculate" button to click.

The calculator includes a Use normality checkbox that switches the displayed units from mol/L to eq/L. For 1:1 reactions N = M; for n:1 reactions (H₂SO₄ + 2NaOH) N = n·M. The math is unchanged; the display changes from "mol/L" to "eq/L".

The formulas

The single equation that drives every acid-base titration in this tool is the stoichiometric conservation equation:

M_a · V_a · n_a = M_b · V_b · n_b

where M is molarity (mol/L), V is volume (L), and n is the stoichiometric coefficient (the number of acidic protons donated by the acid or hydroxide ions accepted by the base). For a monoprotic acid + monoprotic base the coefficients are 1:1 and the equation reduces to the familiar M_a · V_a = M_b · V_b. For a diprotic acid + monoprotic base the ratio is 2:1; for a triprotic acid + monoprotic base the ratio is 3:1. The generalisation covers every acid-base titration that obeys the reaction stoichiometry.

pH at the equivalence point depends on the salt produced:

• Strong + strong (e.g. HCl + NaOH → NaCl): the salt does not hydrolyse, so pH_eq = 7.00 at 25 °C (pKw = 14.00). The strict derivation is from water autoionisation: [H⁺] = [OH⁻] = √Kw = 1.0 × 10⁻⁷ M, so pH = 7.0.
• Weak + strong (e.g. acetic acid + NaOH → sodium acetate): the conjugate base A⁻ hydrolyses basic, A⁻ + H₂O ⇌ HA + OH⁻, with Kb = Kw / Ka. The salt concentration at the equivalence point is C_salt = n_salt / (V_a + V_b), and the standard salt-hydrolysis result is pH_eq = 0.5 · (pKa_acid + pKw + log C_salt). (Harris, Quantitative Chemical Analysis, Ch. 16, eq. 16.19.)
• Strong + weak (e.g. HCl + NH₃ → NH₄Cl): the conjugate acid BH⁺ hydrolyses acidic, BH⁺ ⇌ B + H⁺, with Ka = Kw / Kb. The mirror case gives pH_eq = 0.5 · (pKw − pKb_base − log C_salt), which is below 7.
• Polyprotic: the first equivalence point of a diprotic acid (H₂A → HA⁻ → A²⁻) is approximately 0.5 · (pKa1 + pKa2) from the amphiprotic HA⁻ rule; the second equivalence point of a triprotic acid is 0.5 · (pKa2 + pKa3). The intermediate amphiprotic region is the pH buffer around pKa_i.

Henderson-Hasselbalch at half-equivalence. For a weak acid + strong base titration, at the half-equivalence point [A⁻] = [HA] exactly, so pH = pKa. This is a standard teaching result (Harris, Ch. 16) and is included in the calculator as a sanity-check reminder.

Indicator recommendation. For each indicator in the CRC table, the calculator computes ΔpH = |pH_eq − transition|. The indicator with the smallest ΔpH is the best match. A small ΔpH means the colour change is centred exactly on the equivalence-point jump, the titration curve's steepest region, which minimises the visual error between the observed endpoint and the true equivalence point.

Normality vs molarity. N = M · n (equivalents per mole). For HCl + NaOH n = 1 on both sides, so N = M. For H₂SO₄ + 2NaOH n = 2 on the acid side, so N_acid = 2 · M_acid. The conservation equation is identical when stated in equivalents (N_a · V_a = N_b · V_b); the molarity form just carries the explicit n coefficients.

Worked examples

Example 1, Strong + strong 1:1 (the standard case). 50.0 mL of 0.100 M HCl is titrated with 0.100 M NaOH. The stoichiometry is 1:1, so the conservation equation is M_a · V_a = M_b · V_b. Solving for V_b gives V_b = (0.100 · 50.0) / 0.100 = 50.00 mL. The moles reacted on each side are n = M · V / 1000 = 0.100 · 0.050 = 5.00 × 10⁻³ mol = 5.00 mmol. The pH at the equivalence point is 7.00 (strong + strong, the salt NaCl does not hydrolyse). The moles of acid = moles of base = 5.00 mmol as a cross-check.

Example 2, Weak acid + strong base (acetic acid benchmark). 25.0 mL of 0.200 M acetic acid (CH₃COOH, Ka = 1.8 × 10⁻⁵, pKa = 4.74) is titrated with 0.100 M NaOH. V_b = (0.200 · 25.0) / 0.100 = 50.00 mL. At equivalence, the total volume is 75.0 mL, and the salt concentration is C_salt = (0.200 · 0.025) / 0.075 = 6.67 × 10⁻² M. The pH at equivalence is pH_eq = 0.5 · (4.74 + 14.00 + log 0.0667) = 0.5 · (4.74 + 14.00 − 1.176) = 0.5 · 17.564 = 8.78. Half-equivalence volume is 25.00 mL of NaOH; pH at half-equivalence is pH = pKa = 4.74 exactly. The closest indicator is thymol blue (transition 8.9, ΔpH ≈ 0.12), with phenolphthalein (8.2, ΔpH ≈ 0.58) as a near-second choice.

Example 3, Unknown analyte concentration. A 25.0 mL sample of HCl is titrated with 50.0 mL of 0.100 M NaOH to the bromothymol blue endpoint. The unknown is the analyte concentration M_a. The conservation equation is M_a · V_a = M_b · V_b (1:1), so M_a = (0.100 · 50.0) / 25.0 = 0.200 M. The moles reacted are n = M_a · V_a = 0.200 · 0.025 = 5.00 mmol. This is the standard "what is the concentration?" calculation in quantitative analysis.

Example 4, Polyprotic (H₂SO₄ + 2NaOH). 25.0 mL of 0.050 M sulfuric acid is titrated with 0.100 M NaOH. Stoichiometric ratio is 2:1 (H₂SO₄ donates 2 H⁺). The first equivalence volume is V_b = (M_a · V_a · n_a) / (M_b · n_b) = (0.050 · 25.0 · 2) / (0.100 · 1) = 25.00 mL. At the first equivalence point, the pH is approximately 0.5 · (pKa1 + pKa2) = 0.5 · (−3 + 1.99) = −0.50 (the first pKa of H₂SO₄ is negative because the first proton is fully dissociated). The second equivalence point is at V_b = 50.00 mL, and the solution contains Na₂SO₄ which is essentially neutral (pH ≈ 7.0). The pKa values used are the CRC Handbook values pKa1 = −3 (estimated) and pKa2 = 1.99.

Example 5, Strong + weak back-titration (HCl + NH₃). 25.0 mL of 0.100 M HCl is titrated with 0.100 M NH₃ (Kb = 1.8 × 10⁻⁵, pKb = 4.75). V_b = (0.100 · 25.0) / 0.100 = 25.00 mL. At equivalence, the salt is NH₄Cl, and the BH⁺ ⇌ B + H⁺ hydrolysis gives pH_eq = 0.5 · (14.00 − 4.75 − log 0.0500) = 0.5 · (14.00 − 4.75 + 1.301) = 0.5 · 10.551 = 5.28. The indicator recommendation is methyl orange (transition 3.7, ΔpH ≈ 1.58) over bromothymol blue (7.0, ΔpH ≈ 1.72), for strong + weak systems the appropriate indicator is the acidic-range one.

Where it shows up

Chemistry teaching labs. Acid-base titration is the canonical undergraduate experiment: standardisation of NaOH against potassium hydrogen phthalate (KHP), determination of HCl in gastric juice, aspirin purity by back-titration with NaOH, and carbonate analysis by HCl titration. The equivalence-point equation and the indicator-selection reasoning are specifically taught in the first- and second-year analytical chemistry curriculum.

Food and beverage science. Titratable acidity (TA) in wine, juice, and vinegar is an acid-base titration result, the number of mL of 0.1 N NaOH required to neutralise a 10 mL juice sample to pH 8.2, expressed in g/L of tartaric acid equivalence. Vitamin C (ascorbic acid) determination is a 2,6-dichloroindophenol titration; the iodine value of fats and oils is a redox titration that follows the same stoichiometric framework.

Water and wastewater treatment. Alkalinity titration (H₂SO₄ to pH 4.5) and hardness titration (EDTA with Eriochrome Black T) are canonical Standard Methods for the Examination of Water and Wastewater. The alkalinity reading tells operators how much lime to dose; the hardness reading tells water-softener operators when to regenerate ion-exchange columns.

Pharmaceutical analysis. Active-ingredient assays, content-uniformity testing, and dissolution testing all rely on acid-base titration. The United States Pharmacopeia (USP) monographs call out specific indicators and endpoints for each method, for example, aspirin content by NaOH back-titration with phenolphthalein endpoint, and sodium bicarbonate tablets by HCl titration with methyl orange endpoint.

Soil and agricultural chemistry. Lime requirement (the amount of agricultural lime needed to raise soil pH to a target) is computed from a buffer titration. Cation exchange capacity (CEC) is measured by ammonium acetate displacement followed by titration of the displaced ammonia. Buffer pH tests like the Adams-Evans and Shoemaker-McLean-Pratt (SMP) buffer use the same neutralisation framework.

Dairy and brewing. The Dornic scale for milk acidity is a 0.111 N NaOH titration (1°D = 0.1 g/L lactic acid). Wort pH and beer colour titrations guide mash and kettle decisions in brewing. Cheese makers monitor titratable acidity during fermentation to schedule the renneting step.

Environmental monitoring. Acidity in acid mine drainage (AMD), total Kjeldahl nitrogen (after digestion), chloride by Mohr titration, and biochemical oxygen demand (BOD) all use the same stoichiometric framework. The calculator's normality support helps move between titration conventions used in different regulatory methods.

Common mistakes

Mixing up normality and molarity. For a 1:1 acid-base reaction, N = M mole for mole. For an n:1 reaction (H₂SO₄ + 2NaOH, H₃PO₄ + 3NaOH), N_acid = n · M_acid but N_base = M_base. Always state which you mean when reporting a result. The "Use normality" toggle in the calculator is display-only; the underlying math is the same.

Ignoring temperature on Kw. The neutral pH (= 0.5 · pKw) shifts with temperature: 7.47 at 0 °C, 7.00 at 25 °C, 6.81 at 37 °C, 6.14 at 100 °C. A calibration done at 25 °C and used at 37 °C will drift; a calibration at 100 °C would be off by nearly a full pH unit. For accurate work, calibrate at the working temperature.

Choosing the wrong indicator. Phenolphthalein (transition ≈ 8.2) is right for weak acid + strong base but wrong for strong acid + weak base (use methyl orange, transition ≈ 3.7). Litmus (4.5 to 8.3) is a classic all-purpose indicator but it has a wide transition range and a large visual error. The calculator's indicator-recommendation table ranks the standard CRC list by smallest ΔpH from the computed pH_eq.

Forgetting the stoichiometry ratio. Treating H₂SO₄ as 1:1 with NaOH underestimates the equivalence volume by a factor of 2 (the trickiest polyprotic slip). Treating H₃PO₄ as 1:1 misses both the first equivalence point (at 1 H⁺ per molecule) and the second equivalence point (at 2 H⁺ per molecule).

Reading the endpoint instead of the equivalence point. The indicator changes colour at the endpoint, not the equivalence point. The two differ by the indicator's transition range. The closer the indicator's transition midpoint is to the true equivalence pH, the smaller the visual error. The recommendation panel minimises this.

Confusing equivalence with neutralisation. "Neutralisation" implies pH 7, but the equivalence point is the stoichiometric point and its pH depends on the salt. A weak acid + strong base titration reaches equivalence at pH > 7; a strong acid + weak base titration reaches equivalence at pH < 7. The wording on a lab report should always be "equivalence point" with the pH specified separately.

Using the Henderson-Hasselbalch equation away from the buffer region. The H-H equation pH = pKa + log([A⁻]/[HA]) is valid only in the buffer region (roughly pKa ± 1). It fails at the equivalence point because the ratio is dominated by the salt hydrolysis, and it fails at the very beginning of the titration because the buffer is too dilute. The calculator uses H-H only at the half-equivalence point, where the result is exact.

Frequently Asked Questions

What is the difference between the equivalence point and the endpoint? The equivalence point is the theoretical titrant volume at which the moles of H⁺ delivered by the acid equal the moles of OH⁻ delivered by the base (scaled by stoichiometric coefficients). The endpoint is the titrant volume at which the indicator changes colour. The two are designed to coincide, the indicator's transition is chosen to bracket the steep pH jump at the equivalence point, but the residual difference is the titration error. A good indicator (small ΔpH) keeps the error below 0.1 mL on a 50 mL titration.

What is the difference between molarity and normality? Molarity is moles of solute per litre of solution (mol/L). Normality is equivalents of solute per litre of solution (eq/L); an equivalent is the mass or moles of solute that provides one mole of H⁺ (for acids), one mole of OH⁻ (for bases), or one mole of electrons (for redox). For HCl + NaOH, N = M on both sides. For H₂SO₄ + 2NaOH, N_acid = 2 · M_acid. The conservation equation is N_a · V_a = N_b · V_b, which is the same as M_a · V_a · n_a = M_b · V_b · n_b in molarity form.

Why is the pH at the equivalence point above 7 for weak acid + strong base? Because the salt of a weak acid + strong base (e.g. sodium acetate, NaCH₃COO) hydrolyses basic: the acetate ion is the conjugate base of a weak acid, so it reacts with water to produce OH⁻, raising the pH above 7. The exact pH depends on the salt concentration and the weak acid's Ka. The general formula is pH_eq = 0.5 · (pKa_acid + pKw + log C_salt) where C_salt is the salt concentration at the equivalence point.

Can this calculator handle polyprotic titrations? Yes. The polyprotic mode handles H₂SO₄ (diprotic, two equivalence points), H₃PO₄ (triprotic, three equivalence points), H₂CO₃ (diprotic), and oxalic acid (diprotic). The stoichiometry ratio is auto-set to the number of acidic protons and the calculator reports the pH at the first equivalence point (≈ 0.5 · (pKa1 + pKa2) from the amphiprotic rule) and, for triprotic acids, the pH at the second equivalence point (≈ 0.5 · (pKa2 + pKa3)).

What indicator should I use for a weak acid + strong base titration? Phenolphthalein (transition 8.0 to 10.0, midpoint 8.2) is the classic choice for weak acid + strong base. For a pKa near 4.7 (acetic acid), the equivalence pH is around 8.8 and the closest indicator is thymol blue (transition 8.0 to 9.6, midpoint 8.9). The calculator's recommendation table ranks the indicators by smallest ΔpH from the computed pH_eq.

What indicator should I use for a strong acid + weak base titration? Methyl orange (transition 3.1 to 4.4, midpoint 3.7) is the standard choice for strong acid + weak base. The equivalence pH sits below 7 and the indicator's transition is in the acidic range. Phenolphthalein (transition 8.2) is wrong, it would change colour well past the equivalence point, producing a large visual error.

How accurate are the results? Mathematically, the calculator is accurate to about 15 significant digits of IEEE-754 double-precision floating-point resolution. The accuracy of a real-world answer depends on the accuracy of the inputs: the purity of the standard reagent (typically 99.95% for A.C.S. grade), the volumetric accuracy of the burette (±0.05 mL on a 50 mL Class A burette, or 0.1%), the temperature control of the solution (0.1% on the pKw correction), and the calibration of the indicator or pH electrode. For most lab and educational purposes the results are accurate to 3 to 4 significant figures, more than adequate for analytical work.

Can this calculator be used for redox or complexometric titrations? Not directly. The conservation equation M_a · V_a · n_a = M_b · V_b · n_b is universal to every titration type (acid-base, redox, complexometric, precipitation), but the n coefficients are different. For redox, n is the number of electrons transferred per mole (e.g. n = 5 for MnO₄⁻ + 5e⁻ → Mn²⁺). For complexometric, n is the ligands donated per mole (n = 1 for EDTA most commonly). The user can plug the right n value into the stoichiometry ratio field and the math works, but the pH-equivalence calculation is mode-specific to acid-base and would not be meaningful for a redox endpoint.

How does this calculator handle the temperature dependence of Kw? It assumes 25 °C (pKw = 14.00) by default. The Kw dependence on temperature is real but small: Kw ≈ 1.14 × 10⁻¹⁵ at 0 °C (pKw ≈ 14.94), 2.4 × 10⁻¹⁴ at 37 °C (pKw ≈ 13.62), and 5.1 × 10⁻¹³ at 100 °C (pKw ≈ 12.29). For educational and most bench work the 25 °C default is adequate. For temperature-sensitive work, the user should adjust the indicator selection and the pH-equivalence calculation to the working temperature.

**Q:**Can the Titration Calculator be used for professional or commercial purposes?A: Yes, the Titration Calculator provides mathematically correct results that are suitable for professional, commercial, and educational use. For the Titration Calculator, For the Titration Calculator, For high-stakes applications (medical, legal, financial), verify results with a domain expert. For the Titration Calculator, the Titration Calculator formulas used are well-established and validated against reference standards.

**Q:**For the Titration Calculator, How often are the underlying formulas updated?A: the Titration Calculator formulas are based on established scientific, mathematical, or industry-standard references and rarely require updates. When standards change (e.g., new physical constants, revised tax brackets, updated standards), the Titration Calculator is updated to reflect the current authoritative source. For the Titration Calculator, For the Titration Calculator, Each calculator's references section lists the specific sources used.

References

• Harris, D. C. Quantitative Chemical Analysis, 10th ed., W. H. Freeman (2019). Standard undergraduate reference for acid-base titration theory, salt hydrolysis, indicator selection, and the Henderson-Hasselbalch equation.
• Skoog, D. A., West, D. M., Holler, F. J., & Crouch, S. R. Fundamentals of Analytical Chemistry, 9th ed., Cengage (2014). Canonical analytical chemistry textbook covering titration stoichiometry, equivalence-point derivations, and polyprotic systems.
• IUPAC. Compendium of Chemical Terminology (Gold Book), 2nd ed., online at goldbook.iupac.org. The IUPAC Gold Book is the international authority on chemical terminology; entries "titration", "equivalence point", "indicator", and "pH" are cited.
• CRC Handbook of Chemistry and Physics, 102nd ed., Section 8: "Indicator pH Ranges and Colour Changes". The standard reference for acid-base indicator pKa values and transition ranges.
• Christian, G. D. Analytical Chemistry, 7th ed., Wiley (2013). Covers acid-base titration, salt hydrolysis, polyprotic systems, and the equivalence-point pH derivation for each mode.
• Bates, R. G. Determination of pH: Theory and Practice, 2nd ed., Wiley (1973). Authoritative reference on pH measurement, the operational definition of pH, and the temperature dependence of Kw.