C1V1 = C2V2 Calculator for Dilution

The C1V1 = C2V2 calculator finds the volume of a concentrated starting solution needed to prepare a target solution by dilution. Enter the starting concentration, starting volume, and target concentration or target volume; it returns the remaining value using the dilution equation.

Formula

The dilution equation is C1 × V1 = C2 × V2. Solving for the final volume gives V2 = (C1 × V1) / C2.

• C1 is the starting solution concentration, in mol/L.
• V1 is the volume of starting solution used, in mL.
• C2 is the target concentration after dilution, in mol/L.
• V2 is the total final solution volume, in mL.

The calculator uses the same volume unit for V1 and V2, so the units cancel in the ratio. The second output is the calculated diluent volume, V2 − V1. It assumes the starting solution is part of the final volume and that volumes are additive. The square-root term makes the calculator reject a target volume smaller than the starting volume, because that would not describe adding diluent.

Worked Example

Using the calculator’s defaults, the starting solution is 1 mol/L, the starting volume is 100 mL, and the target concentration is 0.1 mol/L.

1. Write the equation: V2 = (C1 × V1) / C2.
2. Substitute the values: V2 = (1 mol/L × 100 mL) / 0.1 mol/L.
3. Cancel mol/L and calculate: V2 = 100 / 0.1 mL = 1000 mL.
4. Calculate diluent volume: 1000 mL − 100 mL = 900 mL.

The result is a final volume of 1000.00 mL, with 900.00 mL of diluent added under the calculator’s volume-additivity assumption.

Assumptions

• The dissolved substance remains in the solution during dilution; no chemical reaction, precipitation, or loss changes the amount of solute.
• Concentrations use the same basis and units, here mol/L.
• The requested final volume is at least the volume of starting solution.
• Volumes are treated as additive. Some mixtures can contract or expand, so measured final volume may differ slightly.
• This is study and lab-planning arithmetic, not a substitute for a validated method. For bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

How to Use the Calculator

Enter the concentration of the solution you have as C1, the amount of that solution you plan to use as V1, and the desired final concentration as C2. The first result is the total final volume needed. The second result is the diluent volume implied by subtracting V1 from that final volume.

• Use a concentration unit consistently for both concentration entries. This calculator accepts mol/L, not mixed units such as mol/L for C1 and mmol/L for C2.
• Use the same volume unit for V1 and the returned V2. The calculator displays both in mL.
• Enter positive concentrations and a nonnegative starting volume. A zero target concentration is not valid for this calculation because it would require division by zero.
• Check that the calculated final volume is practical for your vessel and method before planning the dilution.

What the Equation Means

Dilution lowers concentration by distributing the same amount of solute through a greater final volume. Concentration multiplied by volume represents the amount of solute, provided the concentration is expressed as amount per volume and the units are compatible. Since dilution does not itself remove solute, the amount before and after is equal: C1V1 = C2V2.

For example, lowering concentration by a factor of ten requires ten times the final volume if all of the starting aliquot is retained. The calculator’s defaults illustrate this: 100 mL of a 1 mol/L solution contains the same solute amount as 1000 mL at 0.1 mol/L. The added diluent is the difference between the final volume and the starting aliquot, not the final volume itself.

Common Mistakes and Limits

• Confusing final volume with diluent volume: V2 is the total mixture volume. V2 − V1 is the calculated diluent amount. A target of 1000 mL does not mean adding 1000 mL of water to the starting solution.
• Mixing concentration units: Convert units before using the equation. For instance, 100 mmol/L equals 0.1 mol/L. Putting 100 and 1 into the calculator without converting would produce a result wrong by a factor of 1000.
• Using the wrong volume: V1 means the volume of starting solution taken, while V2 means the final total volume. Do not substitute the amount of diluent for either one.
• Rounding too early: Keep extra digits during intermediate calculations, then round to a precision justified by the input measurements and method.
• Assuming all mixtures are perfectly additive: The equation conserves solute amount, but it does not account for volume changes on mixing, temperature effects, evaporation, or chemical changes. If an exact final volume matters, use the applicable lab method and bring the mixture to that final volume as directed by the method.

This equation is not appropriate when concentration changes because of a reaction, selective loss, precipitation, or a change in the amount of solute. It also does not calculate a mass to weigh from a solid reagent; that requires the substance’s molar mass and a separate amount-of-substance calculation.

Frequently Asked Questions

What does C1V1 = C2V2 mean?
C1V1 = C2V2 states that the amount of solute before and after a simple dilution is the same. C represents concentration, and V represents solution volume.

How do I calculate V1 instead?
Rearrange the equation to V1 = (C2 × V2) / C1. This calculator specifically solves for V2 from C1, V1, and C2.

Is V2 the amount of water to add?
No. V2 is the final total volume. Under the calculator’s assumption, the diluent volume is V2 − V1.

Can I use different units for C1 and C2?
Convert one concentration so both use the same unit first. For example, convert mmol/L to mol/L by dividing by 1000.

Can this formula be used for serial dilutions?
Yes, for each individual dilution step if the solute amount is conserved and each step’s starting concentration and volume are known. Calculate each stage separately; do not treat the final concentration as though it came from one step unless the combined dilution factor is calculated correctly.

Related

• Dilution Formula Calculator: C1V1 = C2V2 for Molarity
• Dilution Factor Calculator: Final Molarity From Volumes
• Serial Dilution Calculator: Molar Concentration After n Steps

in c1 | Starting concentration, C1 | mol/L | 1 | 0
in v1 | Starting solution volume, V1 | mL | 100 | 0
in c2 | Target concentration, C2 | mol/L | 0.1 | 0
out v2 | Final solution volume, V2 | mL | c1 * v1 / c2 | 2
out dv | Diluent volume to add | mL | v2 - v1 | 2