C1V1 = C2V2 Equation: How to Use It

The c1v1 = c2v2 equation calculates how much of a concentrated solution to use when making a more dilute solution. Enter the starting concentration, the target concentration, and the final volume to find the starting-solution volume required; the calculator also reports the diluent volume to add. Use it only when both concentrations use the same units and the diluted substance is conserved.

Formula

The dilution equation is C1 × V1 = C2 × V2. Rearranging for the volume of starting solution gives V1 = (C2 × V2) / C1.

• C1 is the starting solution concentration in mol/L.
• V1 is the volume of starting solution to measure, in mL.
• C2 is the desired final concentration in mol/L.
• V2 is the desired final solution volume in mL.

The units for C1 and C2 must match; the volume units for V1 and V2 must also match. This calculator uses mL for both volumes, so no volume conversion is needed in the equation. The second output, Vd, is V2 − V1, an ideal estimate of the amount of diluent. In careful solution preparation, add diluent until the total solution reaches V2 rather than assuming that separately measured liquid volumes are perfectly additive.

Worked Example

Using the calculator defaults, prepare 100 mL of a 0.1 mol/L solution from a 1 mol/L starting solution.

1. Identify the values: C1 = 1 mol/L, C2 = 0.1 mol/L, and V2 = 100 mL.
2. Substitute into the rearranged equation: V1 = (0.1 mol/L × 100 mL) / (1 mol/L).
3. Calculate: V1 = 10 mL. The units mol/L cancel, leaving mL.
4. Estimate diluent: Vd = 100 mL − 10 mL = 90 mL.

The calculator reports a starting-solution volume of 10.00 mL and an ideal diluent estimate of 90.00 mL. In practice, measure 10.00 mL of the starting solution and add diluent until the final volume is 100 mL.

Assumptions

• The starting solution contains the same dissolved substance as the target solution, and dilution does not remove or chemically consume it.
• C1 and C2 are expressed in the same concentration units and refer to the same concentration basis.
• The final volume means total solution volume, not the volume of diluent alone.
• The equation treats the dilution as ideal for ordinary preparation arithmetic; it does not account for volume contraction, reaction, evaporation, or measurement uncertainty.
• This is study and lab-planning arithmetic, not guidance for clinical, medication, or animal use.

What You’ll Need

• The starting concentration, C1, from a reliable label, preparation record, or assigned problem.
• The target concentration, C2, and the intended final solution volume, V2.
• A calculator or the calculator fields above. For bench work, use suitable measuring equipment and follow your lab method, the safety data sheet (SDS) and your supervisor.

Step-by-Step

1. Check that this is a dilution. The target concentration must be no greater than the starting concentration. If C2 is greater than C1, the equation would require more starting solution than the final volume; you need a stronger starting solution or a different preparation plan.
2. Choose the concentration units. Write C1 and C2 in the same units, such as mol/L, g/L, or mg/mL. The calculator fields are set to mol/L, so convert other units before entering values. For instance, 100 mmol/L is 0.1 mol/L.
3. Set the desired final volume. Enter V2 in mL. This is the volume of the complete, diluted solution, not the volume of water or other diluent by itself.
4. Enter the three values. Put the starting concentration in C1, the desired concentration in C2, and the final volume in V2. The calculator finds V1 using C2 × V2 / C1.
5. Read the required starting-solution volume. V1 is the portion of the concentrated solution needed. If the answer is very small compared with what you can measure accurately, choose a larger final batch or use a suitable validated intermediate dilution.
6. Prepare to the final volume. Transfer the calculated portion of starting solution, then add diluent until the solution reaches the specified final volume. Mix as directed by the applicable lab method. Do not simply add the full Vd estimate if the procedure requires bringing the mixture to a calibrated final volume.
7. Check the result. The dilution factor is C1/C2. Here it is 1/0.1 = 10, so the starting solution makes up one tenth of the final volume: 10 mL in 100 mL. This independent check should agree with V1.

Common Mistakes

• Mixing concentration units: Using C1 in mol/L and C2 in mmol/L without conversion makes the result wrong by a factor of 1,000. Convert one value so both use the same unit before calculating.
• Using the diluent volume as V2: V2 is the total final solution volume. If you want 100 mL of final solution, enter 100 mL—not the amount of water you expect to add.
• Reversing C1 and C2: C1 is the more concentrated starting solution; C2 is the desired, usually lower, final concentration.
• Rounding too early: Keep sufficient precision in V1 during the calculation, then round to match the precision of your measurement method. Extra decimal places do not make an imprecise measurement accurate.
• Treating diluent volume as exact: V2 − V1 is a useful ideal estimate, but liquid volumes may not add exactly. When final volume matters, bring the mixture to the required total volume.
• Ignoring the concentration basis: The equation works only when the two concentration values describe the same substance on a consistent basis. Do not directly compare mass concentration with molar concentration without converting appropriately.

Tips

• Write units beside each value before substituting them. Matching units make it easier to spot errors.
• Use the rearranged equation V1 = C2V2/C1 when solving by hand. Check that increasing C2 or V2 increases the required V1, while increasing C1 decreases it.
• For a convenient scale-up, multiply both V1 and V2 by the same factor. The concentration ratio stays unchanged.
• Plan around measurement accuracy. If the calculated V1 is too small to measure reliably, make a larger final volume or use an appropriate intermediate solution under an approved method.
• Record the starting concentration, target concentration, final volume, units, and calculation so the preparation can be checked or repeated.

Troubleshooting

• The calculator says it cannot compute: Check that C2 is not greater than C1 and that all entries are nonnegative. A more concentrated target cannot be made by dilution alone.
• The answer is unexpectedly large: Check for mismatched units, a misplaced decimal point, or an incorrect starting concentration. Confirm whether a value is in mol/L, mmol/L, g/L, or another unit.
• The calculated V1 is greater than V2: This indicates an invalid dilution input, commonly because C2 exceeds C1 or the concentrations are in different units. Correct the inputs rather than using a negative diluent volume.
• The expected final concentration is not obtained: Verify the starting concentration and measurement volumes, ensure V2 was treated as the total final volume, and mix as required. Measurement uncertainty, evaporation, degradation, or an incorrect concentration label can also affect the result.
• The required volume is below your measuring range: Do not round it to zero or guess. Increase the batch size or consult the approved method for an intermediate dilution and suitable measurement approach.

Frequently Asked Questions

What does C1V1 = C2V2 mean?
It states that the amount of dissolved substance is conserved during a simple dilution: starting concentration times starting volume equals final concentration times final volume.

How do I solve C1V1 = C2V2 for V1?
Divide both sides by C1: V1 = C2 × V2 / C1. Keep the concentration units consistent and use matching volume units.

Can I use this equation for a target concentration higher than the stock?
No. Dilution lowers concentration. If C2 is higher than C1, V1 would exceed V2; a suitable more concentrated starting solution or another method is needed.

Does V2 mean the amount of water to add?
No. V2 is the final total solution volume. V2 − V1 estimates the diluent volume, but for precise preparation bring the mixture to V2.

Can I use different units for C1 and C2?
Not directly. Convert them to the same units first. For example, convert mmol/L to mol/L by dividing by 1,000.

Does the equation apply to every mixture?
It applies to straightforward dilution when the dissolved substance is conserved. It does not account for chemical reactions, precipitation, degradation, or non-ideal volume changes.

Related

• Find v1 in c1v1 = c2v2
• C1V1 C2V2 Formula for Dilution Calculations
• Sample Dilution Factor Calculator and Formula

in c1 | Starting concentration C1 | mol/L | 1 | 0
in c2 | Target concentration C2 | mol/L | 0.1 | 0
in v2 | Final solution volume V2 | mL | 100 | 0
out v1 | Starting solution volume V1 | mL | c2 * v2 / c1 | 2
out vd | Diluent volume (ideal estimate) | mL | v2 - v1 | 2