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🧪 Analytical

Titration Calculator

Find an unknown acid or base concentration — or the volume — at the equivalence point. Uses Ca·Va·b = Cb·Vb·a, which reduces to Ca·Va = Cb·Vb (or N₁V₁ = N₂V₂) for a 1:1 reaction.

Equivalence point
Any mole ratio
Solve any value
N₁V₁ = N₂V₂
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Titration — Quick answer

At the equivalence point the acid and base moles match by the reaction ratio. Solve the unknown concentration from the other three values.

Ca·Va·b = Cb·Vb·a → Ca = Cb·Vb·a / (Va·b)
1:1 reaction: Ca·Va = Cb·Vb = N₁V₁ = N₂V₂

Worked example: 25 mL acid, endpoint at 20 mL of 0.1 M base, 1:1. Ca = 0.1 × 20 / 25 = 0.08 M.

0.1 M base titrating 25 mL of acid (1:1)

Base usedAcid concNote
10 mL0.040 Mweak acid soln
20 mL0.080 Mexample
25 mL0.100 Mequal volume

Used for: standardising solutions, lab analysis, neutralisation.

🧪 Titration Calculator

Leave the one unknown blank. Enter the mole ratio (acid : base) — 1 and 1 for HCl + NaOH.

Acid conc Ca
Base conc Cb
Acid volume Va
Base volume Vb

⚠️ Set the coefficients from the balanced equation. H₂SO₄ + 2 NaOH means a = 1, b = 2. Both volumes must use the same unit; the result concentration is the same whether you enter mL or L.

A titration finds an unknown concentration by reacting it, drop by drop, with a solution of known concentration until the reaction is exactly complete — the equivalence point. At that moment the moles of acid and base are balanced by the reaction's mole ratio, which gives the working equation Ca·Va·b = Cb·Vb·a. For the common 1:1 case it simplifies to Ca·Va = Cb·Vb, the same relationship written as N₁V₁ = N₂V₂ when you use normality. Rearrange it to solve for whichever of the four quantities you didn't measure.

Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: stoichiometric equivalence at the titration endpoint.

The titration equations

Equivalence
(Ca × Va) / a = (Cb × Vb) / b
Unknown acid conc
Ca = Cb × Vb × a / (Va × b)
1:1 / normality form
Ca × Va = Cb × Vb (or N₁V₁ = N₂V₂)

The coefficients a and b come straight from the balanced neutralisation equation: they are the moles of acid and base that react together. When a = b the equation collapses to a simple cross-multiplication. Because volume sits on both sides, its unit cancels — millilitres are fine. To report the moles that actually reacted, convert a volume to litres and multiply by its molar concentration.

Worked example — standardising an acid

Scenario: A 25 mL sample of hydrochloric acid is titrated with 0.1 M sodium hydroxide. The indicator changes colour after 20 mL of base. The reaction HCl + NaOH is 1:1. What is the acid concentration?

Acid concentration
Ca = (0.1 × 20 × 1) / (25 × 1) = 2 / 25 = 0.08 M
Moles reacted
0.08 × 0.025 L = 0.002 mol acid = 0.1 × 0.020 L base ✓

The acid is 0.08 M. Both half-reactions supply 0.002 mol, confirming the balance. Had this been sulfuric acid (a = 1, b = 2), the same 20 mL of base would only neutralise half as much acid per millilitre, so the calculated Ca would be 0.04 M instead — which is exactly why the mole ratio must be set correctly before reading the answer.

Frequently Asked Questions

How do I find the unknown concentration?

Ca = Cb·Vb·a/(Va·b). For 1:1, Ca·Va = Cb·Vb. e.g. 0.1 M × 20 mL ÷ 25 mL = 0.08 M.

What is N₁V₁ = N₂V₂?

The normality form — equivalents already include the proton/electron count, so coefficients vanish. Use normality, not molarity.

Equivalence point vs endpoint?

Equivalence = moles exactly matched (what we calculate). Endpoint = the indicator colour change you watch for.

Why does the mole ratio matter?

Diprotic acids like H₂SO₄ need 2 NaOH per acid (a=1, b=2). Ignoring it gives an answer off by 2×.

Do volumes need to be in litres?

No — the unit cancels. Use mL on both sides. Litres are only needed if you want the moles reacted.

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