C1V1 = C2V2 Calculator for Dilution

The C₁V₁ = C₂V₂ calculator finds how much of a starting solution is needed to prepare a more dilute solution of a chosen volume and concentration. Enter the initial concentration (C₁), the desired final concentration (C₂), and the final volume (V₂); it returns the volume of starting solution to use (V₁), plus the volume of diluent to add.

Formula

The dilution equation is C₁V₁ = C₂V₂. Solving for the volume of starting solution gives V₁ = C₂V₂ / C₁. The calculator then finds the diluent volume by subtracting the starting-solution volume from the desired final volume.

• C₁ is the concentration of the starting, more concentrated solution, in millimolar (mM).
• V₁ is the volume of starting solution required, in millilitres (mL).
• C₂ is the desired final concentration, in mM.
• V₂ is the desired final solution volume, in mL.
• Diluent volume is V₂ − V₁, in mL. It is the amount to add if the starting solution and diluent volumes are treated as additive.

The equation assumes the amount of solute is conserved during dilution: the solute amount in the aliquot taken from the starting solution equals the solute amount in the final mixture. Concentration units must match on both sides. The calculator uses mM for both concentrations and mL for both volumes, so no conversion factor is needed. You may use another concentration unit and another volume unit in the same way, provided each pair matches.

Worked Example

Using the default values, C₁ = 100 mM, C₂ = 10 mM, and V₂ = 100 mL:

1. Calculate the starting-solution volume: V₁ = C₂V₂ / C₁ = (10 mM × 100 mL) / 100 mM = 10 mL.
2. Calculate the diluent volume: V₂ − V₁ = 100 mL − 10 mL = 90 mL.

The calculator reports 10.00 mL of starting solution and 90.00 mL of diluent. The final mixture is 100 mL at 10 mM, assuming the volumes combine additively and the starting solution concentration is accurate.

Assumptions

• The starting and final concentrations use the same units, and both volumes use the same units.
• The solution is diluted without losing or adding solute through a reaction, precipitation, evaporation, or transfer loss.
• The target concentration is lower than the starting concentration, and the target volume is the final solution volume.
• Volumes are treated as additive. For precise work, prepare to the final volume using the relevant lab method rather than assuming that separately measured volumes sum exactly.

How to Use the Result

For the example, measure 10 mL of the 100 mM starting solution, then add diluent until the total solution volume reaches 100 mL. The arithmetic output of 90 mL is the diluent amount only under the additive-volume assumption. If the method calls for a specified final volume, bring the mixture to that final volume instead of treating the calculated diluent amount as an instruction to overfill.

This calculation is useful for planning a one-step dilution when the stock concentration, target concentration, and final volume are known. It does not determine the stock’s actual concentration, account for measurement uncertainty, or select a suitable solvent. The starting concentration must come from a reliable label, preparation record, or independent measurement.

For a series of dilutions, calculate each step from the concentration present at the start of that step. A dilution factor is C₁/C₂, so the example is a 10-fold dilution. If a target requires taking a volume too small to measure reliably, a planned intermediate dilution may improve practical accuracy; each stage still needs its own calculation and appropriate measurement equipment.

Common Mistakes and Limits

• Mixing units: Do not put C₁ in mol/L and C₂ in mM without conversion. For example, 1 mol/L = 1000 mM. Convert first, or express both concentrations in the same unit.
• Using the wrong volume: V₂ is the total final solution volume, not simply the volume of diluent. Using the amount of solvent as V₂ gives the wrong result.
• Reversing initial and final values: C₁ refers to the starting solution and C₂ to the target. For a dilution, C₂ should be no greater than C₁. The calculator rejects a target concentration above C₁.
• Rounding too early: Keep extra digits during intermediate calculations, then round the measured volume to a precision your equipment can support. A displayed value such as 10.00 mL does not mean every setup can measure to 0.01 mL accurately.
• Assuming volumes are always perfectly additive: Mixing can change total volume slightly. In analytical work, the final volume should be established by the prescribed method, not inferred from ideal volume addition.

The C₁V₁ = C₂V₂ relationship describes dilution arithmetic, not chemical compatibility or safety. It cannot correct for a stock that has degraded, an inaccurate concentration, adsorption to a container, or a chemical reaction during mixing. For bench work, follow your lab method, the safety data sheet (SDS), and your supervisor.

Frequently Asked Questions

What does C₁V₁ = C₂V₂ mean?
C₁V₁ represents the amount of solute in the starting-solution portion. C₂V₂ represents the amount of that solute in the final mixture. For simple dilution, those amounts are equal.

How do I calculate V₁?
Rearrange the equation to V₁ = C₂V₂/C₁. Use matching concentration units and matching volume units. The calculator gives V₁ directly.

Can C₂ be greater than C₁?
Not for a dilution: adding diluent cannot make the solution more concentrated than its starting solution. A target above C₁ would require a different approach, such as concentrating or preparing a stronger solution, rather than applying this dilution calculation.

Is V₂ the amount of water or the final volume?
V₂ is the total final solution volume. The calculator’s second result estimates the diluent volume as V₂ − V₁, but actual preparation methods may require bringing the mixture to the final volume rather than adding that exact amount of solvent.

Can I use this formula with different units?
Yes, as long as C₁ and C₂ share a concentration unit and V₁ and V₂ share a volume unit. Convert any mismatched values before calculating; for example, 1 L = 1000 mL and 1 mol/L = 1000 mM.

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 | Initial concentration C1 | mM | 100 | 0
in c2 | Desired concentration C2 | mM | 10 | 0
in v2 | Final solution volume V2 | mL | 100 | 0
out v1 | Starting solution volume V1 | mL | c2 * v2 / c1 | 2
out dil | Diluent volume (V2 - V1) | mL | v2 - v1 | 2