What is the titration formula?

For acid-base: nₐ × Mₐ × Vₐ = n_b × M_b × V_b, where n is the number of protons (or OH groups), M is molarity, and V is volume. Both volumes use the same units (mL or L). For monoprotic acids and bases, simplifies to Mₐ × Vₐ = M_b × V_b.

What is the equivalence point?

The equivalence point is where moles of acid (× protons) equal moles of base (× OH groups). At this point the reaction is stoichiometrically complete. The pH at equivalence depends on the strengths: 7 for strong+strong, >7 for weak acid + strong base, <7 for strong acid + weak base.

What's the difference between equivalence point and endpoint?

Equivalence point is the theoretical stoichiometric balance. Endpoint is where the indicator changes color (or pH probe gives a target reading). A well-chosen indicator makes them nearly identical (<1% titration error); poor choice can shift them significantly.

How do I pick the right indicator?

Pick an indicator whose pKa is close to the expected equivalence point pH. Phenolphthalein (transition pH 8.2–10) is best for strong-base titration of weak acids. Methyl orange (3.1–4.4) for strong-acid titration of weak bases. Bromothymol blue (6.0–7.6) for strong acid + strong base. For polyprotic systems, use multiple indicators or a pH probe.

How accurate is titration?

With a Class A volumetric burette and primary standard: typically ±0.1–0.2% relative error. With visual indicators: ±0.5% from titration error. With pH electrode endpoint detection: ±0.05% achievable. Major error sources: burette calibration, primary standard purity, evaporation during titration, indicator pKa mismatch.

Why do I need to standardize NaOH before using it?

NaOH is hygroscopic (absorbs water from air) and reacts with atmospheric CO₂ to form Na₂CO₃. Both processes change the effective concentration over time. Standardizing against KHP (a primary standard) gives the actual current molarity, which can differ from the label by 1–5% depending on age and storage.

Can I titrate a polyprotic acid?

Yes. For H₂SO₄ (which fully ionizes both protons), use nₐ = 2 in the equation. For H₃PO₄ (which has three distinguishable equivalence points, pKa1 = 2.1, pKa2 = 7.2, pKa3 = 12.4), choose which endpoint you're measuring and adjust nₐ. Or use a pH electrode to map the full curve and identify multiple equivalence points.

Titration Calculator

Q: What's the difference between equivalence point and endpoint?

Equivalence point is the theoretical stoichiometric balance. Endpoint is where the indicator changes color (or pH probe gives a target reading). A well-chosen indicator makes them nearly identical (<1% titration error); poor choice can shift them significantly.

Q: How do I pick the right indicator?

Pick an indicator whose pKa is close to the expected equivalence point pH. Phenolphthalein (transition pH 8.2–10) is best for strong-base titration of weak acids. Methyl orange (3.1–4.4) for strong-acid titration of weak bases. Bromothymol blue (6.0–7.6) for strong acid + strong base. For polyprotic systems, use multiple indicators or a pH probe.

Q: How accurate is titration?

With a Class A volumetric burette and primary standard: typically ±0.1–0.2% relative error. With visual indicators: ±0.5% from titration error. With pH electrode endpoint detection: ±0.05% achievable. Major error sources: burette calibration, primary standard purity, evaporation during titration, indicator pKa mismatch.

Q: Why do I need to standardize NaOH before using it?

NaOH is hygroscopic (absorbs water from air) and reacts with atmospheric CO₂ to form Na₂CO₃. Both processes change the effective concentration over time. Standardizing against KHP (a primary standard) gives the actual current molarity, which can differ from the label by 1–5% depending on age and storage.

Q: Can I titrate a polyprotic acid?

Yes. For H₂SO₄ (which fully ionizes both protons), use nₐ = 2 in the equation. For H₃PO₄ (which has three distinguishable equivalence points, pKa1 = 2.1, pKa2 = 7.2, pKa3 = 12.4), choose which endpoint you're measuring and adjust nₐ. Or use a pH electrode to map the full curve and identify multiple equivalence points.

Perform acid-base titration calculations using Ma x Va = Mb x Vb. Find the unknown concentration or volume at the equivalence point for monoprotic and polyprotic reactions.

Titration is the classical method of determining the concentration of an unknown solution by reacting it with a known one. Drip a standard solution (the "titrant") from a burette into a measured volume of the unknown solution until a color change or pH indicator marks the "endpoint" — the point where the reactants are stoichiometrically balanced. From the volume added and the concentration of the titrant, the unknown concentration follows directly.

The equation behind titration is just stoichiometric bookkeeping: moles of acid = moles of base at the equivalence point (for monoprotic systems), or generalized to nₐ × Mₐ × Vₐ = n_b × M_b × V_b for polyprotic systems where one acid molecule donates n protons (or one base accepts n protons). This calculator handles both cases — enter what you know, pick what to solve for, and you get the missing variable.

Titration is one of the oldest quantitative chemistry techniques, going back to the 1700s. It remains the standard method for measuring acidity (vinegar, wine, pool water), drug content in pharmaceuticals, water hardness, alkalinity in soils, and many other applications. Modern automated titrators do the burette-and-indicator dance with electrodes and software, but the underlying math is unchanged.

Inputs

Solve For

Acid Molarity (Ma) mol/L

Acid Volume (Va) mL

Base Molarity (Mb) mol/L

Base Volume (Vb) mL

Acid Protons (n)

Base OH Groups (n)

Results

Moles Acid

0.00250 mol

Moles Base

0.00250 mol

Base Molarity

0.1000 M

Titration Results

Parameter	Value
Acid Molarity (Ma)	0.1000 mol/L
Acid Volume (Va)	25.00 mL
Acid Protons (n)	1
Base Molarity (Mb)	0.1000 mol/L
Base Volume (Vb)	25.00 mL
Base OH Groups (n)	1
Moles of Acid	0.002500 mol
Moles of Base	0.002500 mol
Equivalents Acid	0.002500 eq
Equivalents Base	0.002500 eq

Last updated: May 28, 2026

Formula

**Acid-base titration equation (monoprotic):** Mₐ × Vₐ = M_b × V_b Where: - **Mₐ, M_b**: molarity of acid and base - **Vₐ, V_b**: volume of acid and base At the equivalence point, moles_acid = moles_base. **Polyprotic (diprotic, triprotic) generalization:** nₐ × Mₐ × Vₐ = n_b × M_b × V_b Where n is the number of acidic protons per acid molecule (or basic OH per base): - nₐ = 1 for HCl, HNO₃, acetic acid - nₐ = 2 for H₂SO₄, H₂CO₃ (diprotic) - nₐ = 3 for H₃PO₄ (triprotic) - n_b = 1 for NaOH, KOH - n_b = 2 for Ca(OH)₂, Mg(OH)₂ **Solving for each variable:** - M_b = (nₐ × Mₐ × Vₐ) / (n_b × V_b) - V_b = (nₐ × Mₐ × Vₐ) / (n_b × M_b) - Mₐ = (n_b × M_b × V_b) / (nₐ × Vₐ) - Vₐ = (n_b × M_b × V_b) / (nₐ × Mₐ) **Example: HCl titrated with NaOH** 50.0 mL of unknown HCl + 0.100 M NaOH → endpoint at 32.4 mL NaOH. Find HCl molarity. - Both monoprotic (n=1 each) - Mₐ = (1 × 0.100 × 32.4) / (1 × 50.0) = **0.0648 M HCl** **Example: H₂SO₄ titrated with NaOH** 25.0 mL of unknown H₂SO₄ + 0.50 M NaOH → endpoint at 30.0 mL NaOH. Find H₂SO₄ molarity. - H₂SO₄ is diprotic (nₐ = 2), NaOH is monoprotic (n_b = 1) - 2 × Mₐ × 25.0 = 1 × 0.50 × 30.0 - Mₐ = (0.50 × 30.0) / (2 × 25.0) = **0.30 M H₂SO₄** **Endpoint vs equivalence point:** - **Equivalence point**: stoichiometric balance, moles_acid × n_a = moles_base × n_b. - **Endpoint**: where the indicator changes color (visual signal). - They should coincide for a well-chosen indicator. The "titration error" is the small difference between them, usually <1%. **Common pH indicators by transition range:** | Indicator | Color change | pH range | |---|---|---| | Methyl orange | red → yellow | 3.1–4.4 | | Bromocresol green | yellow → blue | 3.8–5.4 | | Methyl red | red → yellow | 4.4–6.2 | | Bromothymol blue | yellow → blue | 6.0–7.6 | | Phenolphthalein | colorless → pink | 8.2–10.0 | Pick an indicator with transition range close to the equivalence point pH for accurate endpoint detection. **Equivalence point pH (general rules):** - **Strong acid + strong base**: pH 7 at equivalence (neutral salt) - **Strong acid + weak base**: pH < 7 at equivalence (acidic salt) - **Weak acid + strong base**: pH > 7 at equivalence (basic salt) - **Weak acid + weak base**: depends on relative strengths

How to use this calculator

Identify acid and base, including how many protons each contributes (nₐ for acid, n_b for base).
Enter the three known values; pick which one to solve for.
Volumes can be in any matching units (both mL or both L) — they cancel.
For polyprotic acids, n is the total number of protons that react in the titration window (some titrations only deprotonate to the first equivalence point).
Pick an indicator with pKa near the equivalence point pH; phenolphthalein for strong base + weak acid, methyl orange for strong acid + weak base.
For accurate work, calibrate the burette (gravimetric water deliveries) and standardize the titrant against a primary standard.

Worked examples

Standardizing NaOH against KHP

**Scenario:** Standardize a NaOH solution by titrating against 0.5024 g of potassium hydrogen phthalate (KHP, 204.22 g/mol, monoprotic). Endpoint reached at 27.45 mL of NaOH. **Calculation:** Moles KHP = 0.5024 / 204.22 = 0.002460 mol. At equivalence: moles NaOH = 0.002460 mol. NaOH molarity = 0.002460 / 0.02745 L = 0.0896 M. **Result:** NaOH solution is 0.0896 M (compared to nominal 0.10 M target — the solution is slightly less concentrated, possibly due to CO₂ absorption during storage). KHP is the standard "primary standard" because it's easy to obtain pure, stable, non-hygroscopic, and exactly monoprotic.

Acid content of vinegar

**Scenario:** Titrate 10.0 mL of household vinegar with 0.10 M NaOH. Phenolphthalein endpoint at 41.7 mL. Acetic acid is monoprotic. What's the acetic acid concentration? **Calculation:** Mₐ = (n_b × M_b × V_b) / (nₐ × Vₐ) = (1 × 0.10 × 41.7) / (1 × 10.0) = 0.417 M. To convert to %: 0.417 mol/L × 60.05 g/mol = 25.0 g/L = 2.5 g per 100 mL ≈ 2.5% (w/v) acetic acid. **Result:** This vinegar is 2.5% acetic acid by volume. Commercial labels typically say "5% acidity" which means weight/volume — this sample is a bit weak, possibly diluted with water or near expiration. Standard vinegar is 5–6%; specialty vinegars range 4–8%.

Sulfuric acid in a battery

**Scenario:** Sample 5.0 mL of battery acid (concentrated H₂SO₄), diluted to 250 mL with water. Titrate 25 mL of the diluted sample with 1.0 M NaOH. Endpoint at 39.2 mL. **Calculation:** Diluted H₂SO₄ molarity: nₐ × Mₐ × Vₐ = n_b × M_b × V_b → 2 × Mₐ × 25 = 1 × 1.0 × 39.2 → Mₐ = 39.2 / (2 × 25) = 0.784 M (in diluted sample). Dilution factor: 250/5 = 50×. Original concentration: 0.784 × 50 = 39.2 M H₂SO₄. **Result:** Battery acid is 39.2 M H₂SO₄ (about 95% w/w concentrated sulfuric acid). Consistent with typical lead-acid battery electrolyte (37 M = 33% w/w when discharged, 39 M = 96% w/w when fully charged).

When to use this calculator

**Use titration for quantitative concentration measurement:**

- **Acid-base titration**: most common; vinegar acidity, antacid neutralization capacity, soil pH, drug content. - **Redox titration**: iodometry for vitamin C, KMnO₄ for iron content, Karl Fischer for water content. - **Precipitation titration**: Mohr method for chloride (AgNO₃), Volhard for back-titration. - **Complexometric titration**: EDTA for water hardness (Ca²⁺, Mg²⁺), drug metal content. - **Pharmaceutical assay**: USP titration methods for drug active content. - **Brewing chemistry**: titratable acidity in wine, beer, kombucha. - **Water analysis**: alkalinity (HCl titration), chloride, dissolved CO₂.

**Choosing an indicator:**

| Reaction type | Endpoint pH | Recommended indicator | |---|---|---| | Strong acid + strong base | 7.0 | Bromothymol blue (6.0–7.6) | | Strong acid + weak base (NH₃) | ~5.0 | Methyl red (4.4–6.2) | | Weak acid (acetic) + strong base | ~8.7 | Phenolphthalein (8.2–10.0) | | Diprotic acid first equivalence | depends | Bromocresol green | | Polyprotic with two endpoints | multiple | Two indicators or pH probe |

**Why use pH electrode instead of color indicator:**

- More accurate (±0.01 pH vs ±0.2 for visual). - No color interference (works in colored solutions like wine, juice, urine). - Records full titration curve, not just endpoint — extracts pKa info. - Automation possible (auto-titrators).

**Calibration and standardization:**

- **Primary standards**: KHP (for bases), Na₂CO₃ (for acids). Stable, non-hygroscopic, high purity. - **Standardize the titrant before use**: small concentration drift happens during storage. - **Use a burette calibrated against gravimetric water deliveries** for highest accuracy. - **Run a blank**: subtract titrant volume used by the buffer/water alone.

**Beyond simple endpoint:**

- **Equivalence point** = stoichiometric balance. - **Endpoint** = where indicator changes (close to but not exactly the equivalence point). - **Half-equivalence point**: pH = pKa of weak acid. Useful for measuring pKa. - **Buffer region**: pH changes slowly during initial titration of weak acid; gives buffer capacity.

Common mistakes to avoid

Using the wrong indicator. Methyl orange for a weak acid titration gives early endpoints (acidic transition range catches base buildup too soon).
Forgetting the protonation factor for polyprotic acids. H₂SO₄ has nₐ = 2; using nₐ = 1 gives half the correct concentration.
Mixing up which reactant is in the burette vs flask. Mathematically symmetric, but the burette holds the titrant whose concentration is known.
Reading the burette wrong. Top of meniscus or bottom? Always read from the bottom of the meniscus for transparent solutions.
Adding titrant too fast near the endpoint. The color change is sharp; one extra drop can overshoot significantly. Slow to dropwise near color change.
Not stirring continuously. Local high-titrant pockets cause early indicator response.
Skipping the burette tip air bubble check. An air bubble released during titration adds volume not registered on the meniscus reading.

Frequently Asked Questions

Sources & further reading

SponsoredShop Top Deals on AmazonSupport CalcMountain — browse top-rated products at no extra cost to you.