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Solution Dilution Calculator

Chemistry

Use the C₁V₁ = C₂V₂ dilution equation to find stock volume needed, final concentration, or volume of diluent to add. Works for molarity, normality, and percent solutions.

5 mol/L
mol/L
10 mL
mL
0.5 mol/L
mol/L

Final Volume (V₂)

100
Volume of Diluent to Add
90
Dilution Factor
10

This calculator computes your Final Volume (V₂), Volume of Diluent to Add, Dilution Factor from the values you enter.

Inputs
Initial Concentration (C₁)Volume of Stock Solution (V₁)Target Concentration (C₂)
Outputs
Final Volume (V₂)Volume of Diluent to AddDilution Factor

What is a Solution Dilution?

The Solution Dilution Calculator applies the C₁V₁ = C₂V₂ equation to determine the final volume needed when diluting a solution from a known initial concentration to a target concentration. Given the stock concentration (C₁), the volume of stock taken (V₁), and the target concentration (C₂), it returns the final total volume (V₂), the volume of diluent to add, and the dilution factor.

The equation C₁V₁ = C₂V₂ (also written as n₁ = n₂, meaning moles before = moles after) is derived from the law of conservation of matter. When you dilute a solution, you add solvent — but no solute is added or removed. The total moles of solute in V₁ litres at C₁ mol/L equals the total moles in V₂ litres at C₂ mol/L. This one equation covers the most common question in solution preparation: "I have a concentrated stock — how do I make a working solution at the concentration I need?"

The equation works for molarity (mol/L), percent by volume (% v/v), percent by mass/volume (% w/v), and any other linear concentration unit — as long as C₁ and C₂ use the same unit and V₁ and V₂ use the same unit. It does not directly apply to % w/w (mass percent), which is referenced to solvent mass rather than solution volume.

In Indian chemistry and pharmacy education, C₁V₁ = C₂V₂ is introduced in NCERT Class 12 Chapter 2 and is a foundational equation in all laboratory science courses. Its practical applications span from preparing 0.1 M NaOH from a 10 M stock, to calculating the volume of concentrated HCl needed for a titration experiment, to compounding IV drug solutions in hospital pharmacies across India.

For planning multi-step serial dilutions, see the Serial Dilution Calculator. To start from solid solute rather than a stock solution, use the Concentration Calculator to calculate the initial concentration first.

How to use this Solution Dilution calculator

  1. Record your stock concentration — find C₁ from the label of your stock solution, from a previous preparation, or from the Concentration Calculator if you prepared the stock from a solid.
  2. Enter Initial Concentration (C₁) — type the stock concentration into the Initial Concentration (C₁) field. Use mol/L, %, g/L, or any linear unit — as long as C₂ uses the same unit.
  3. Enter Volume of Stock Solution (V₁) — type the volume of stock solution you will measure out into the Volume of Stock Solution (V₁) field in mL. This is the volume you will pipette or measure.
  4. Enter Target Concentration (C₂) — type the working concentration you want to achieve into the Target Concentration (C₂) field (same units as C₁).
  5. Read Final Volume (V₂) — the highlighted output gives the total final volume in mL. This is the volume to make up to in your volumetric flask.
  6. Add diluent — pour V₁ of stock into your flask, then add the displayed diluent volume (V₂ − V₁) to reach exactly V₂. For multi-step dilutions, use the Serial Dilution Calculator.

Formula & Methodology

Dilution equation:

> C₁V₁ = C₂V₂

Rearranged to find final volume:

> V₂ = (C₁ × V₁) ÷ C₂

Diluent volume:

> V_diluent = V₂ − V₁

Dilution factor:

> DF = C₁ ÷ C₂ = V₂ ÷ V₁

Derivation:

Moles before dilution: n = C₁ × V₁
Moles after dilution: n = C₂ × V₂
Since moles are conserved: C₁V₁ = C₂V₂ ✓

Worked example 1 — Preparing 0.1 M NaOH from 2 M stock:

- C₁ = 2 M, V₁ = 25 mL, C₂ = 0.1 M
- V₂ = (2 × 25) ÷ 0.1 = 500 mL
- Diluent = 500 − 25 = 475 mL water
- DF = 2 ÷ 0.1 = 20-fold dilution
- Method: Measure 25 mL of 2 M NaOH into a 500 mL volumetric flask. Add water to the 500 mL mark.

Worked example 2 — Concentrated HCl to 1 N (for Class 11 practical):

Concentrated HCl = 12 M = 12 N (n-factor = 1). Target: 250 mL of 0.1 N HCl.
- V₁ = C₂V₂ ÷ C₁ = (0.1 × 250) ÷ 12 = 2.08 mL concentrated HCl
- Add 2.08 mL HCl slowly to ~200 mL water, cool, make up to 250 mL

Worked example 3 — IV drug compounding (Indian hospital context):

A patient requires 500 mL of 5% glucose with 20 mEq KCl. Stock KCl injection = 2 mEq/mL (10 mL vial). Volume of KCl to add = C₂V₂/C₁ = (20 mEq ÷ 2 mEq/mL) = 10 mL. Add 10 mL from one vial to the 500 mL glucose bag. Final KCl concentration = 20 mEq ÷ 510 mL ≈ 0.039 mEq/mL.

Frequently Asked Questions

C₁V₁ = C₂V₂ is the dilution equation that states the number of moles of solute is conserved when you dilute a solution — no solute is added or removed, only solvent. C₁ is the initial concentration, V₁ is the initial volume (of stock taken), C₂ is the final concentration, and V₂ is the final total volume. Rearranging: V₂ = C₁V₁/C₂ (find final volume), V₁ = C₂V₂/C₁ (find stock volume needed).
The units must be consistent within each side: C₁ and C₂ must use the same concentration unit (mol/L, %, g/L, mg/mL, ppm — any unit that is linear in amount), and V₁ and V₂ must use the same volume unit (both mL, both L, both µL). The equation does not require any particular unit, just consistency across both concentration values and across both volume values.
V₂ is the total final volume — the combined volume of stock solution plus diluent. The volume of diluent to add is V₂ − V₁. For example, if V₁ = 10 mL of stock and V₂ = 100 mL, you add 90 mL of diluent to the 10 mL of stock to reach 100 mL total. The Solution Dilution Calculator outputs both V₂ and the diluent volume to avoid this confusion.
The equation works for any concentration unit that is proportional to the amount of solute (moles, mass, or particles per unit volume). Molarity (mol/L) is proportional to moles; percent by volume (% v/v) is proportional to volume of solute. Both satisfy the conservation of solute: the total moles (or mass, or volume) of solute in V₁ at C₁ equals the total in V₂ at C₂. The only unit that does not work directly is mass percent (% w/w), which uses solvent mass rather than solution volume.
Always add acid to water — never water to acid. The dissolution of concentrated H₂SO₄ or HCl releases significant heat (enthalpy of dilution); adding water to acid can cause violent boiling and splashing. Calculate the required volume of concentrated acid using V₁ = C₂V₂/C₁, add it slowly to most of the final water volume while stirring, cool if necessary, then make up to the final volume V₂. Always wear PPE (goggles, lab coat, acid-resistant gloves).
Dissolution is the process of dissolving a solid solute in a solvent to create a solution. Dilution is adding more solvent to an existing solution to reduce its concentration. The Concentration Calculator handles dissolution (from mass, molar mass, and volume to molarity); the Solution Dilution Calculator handles dilution (from a prepared solution of known concentration to a more dilute one using C₁V₁ = C₂V₂).
Enter the Initial Concentration (C₁) of your stock, the Volume of Stock Solution (V₁) in mL that you will take, and the Target Concentration (C₂) you want to achieve. The calculator outputs the Final Volume (V₂) in mL you need to make up to, the volume of diluent to add (V₂ − V₁), and the dilution factor. Measure V₁ of stock, place in your flask, then add diluent to reach V₂.
Using C₁V₁ = C₂V₂: V₁ = C₂ × V₂ / C₁ = 0.1 × 1000 / 12 = 8.33 mL of concentrated HCl to make 1 litre of 0.1 M HCl. Measure 8.33 mL of concentrated HCl, add slowly to about 800 mL of water in a 1-litre volumetric flask (acid to water!), cool to room temperature, then make up to 1 litre with water. The Solution Dilution Calculator gives this result directly when you enter C₁ = 12, V₁ = 8.33 mL, C₂ = 0.1.
Yes — the C₁V₁ = C₂V₂ equation applies to any linear concentration unit, including the 1:5 whole blood dilutions used in cell counting (1 part blood + 4 parts diluent = total DF 5) or the 1:200 dilutions used in RBC counting. Enter C₁ = any concentration value (or use 1 for ratio-based dilutions), V₁ = sample volume, and C₂ = C₁/DF to find V₂. This is the same calculation used in Neubauer chamber and automated haematology analyser sample preparation.
The Indian Pharmacopoeia (IP) and FDA India (CDSCO) express drug concentrations in several units depending on the dosage form: mg/mL (injections), % w/v (solutions, eye drops), % w/w (ointments, creams), mg/tablet or mg/capsule (solid dosage forms). For IV preparations, the Solution Dilution Calculator using C₁V₁ = C₂V₂ is the standard method for computing the required volume of concentrated injection to add to an IV bag to achieve the prescribed dose concentration.
The dilution equation C₁V₁ = C₂V₂ is taught in NCERT Class 12 Chemistry Chapter 2 (Solutions) and is also implicit in the volumetric analysis sections of Class 11 practical chemistry. It appears in JEE Main and Advanced as a direct calculation and as part of titration preparation problems. NEET tests it in the context of IV fluid preparation and drug concentration calculations in physiology and pharmacology questions.
Yes — there is no mathematical limit to the dilution factor in the C₁V₁ = C₂V₂ equation. However, at very high dilution factors (>1000×), practical limitations arise: the volume of stock becomes very small (µL range), weighing and pipetting errors become significant, and at extreme dilutions (>10⁸×), statistical effects on particle count become relevant. For dilution factors above ~100, use multi-step serial dilutions (see Serial Dilution Calculator) rather than a single-step dilution to improve accuracy.
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