C1V1 = C2V2 Calculator for Dilution

The C1V1 = C2V2 calculator finds the volume of a starting solution needed to make a chosen volume at a lower concentration, or checks the resulting concentration. Enter the known concentration and volumes in matching units; the calculator returns the missing value using the dilution equation.

Formula

The standard dilution equation is C₁V₁ = C₂V₂. It states that the amount of solute transferred from the starting solution equals the amount in the final diluted solution, assuming no solute is lost.

• C₁ is the starting concentration, in ng/µL here.
• V₁ is the volume of starting solution used, in µL.
• C₂ is the target or final concentration, in ng/µL.
• V₂ is the final total solution volume, in µL.

Solving for the starting volume gives V₁ = C₂V₂/C₁. The calculator’s first result reports this required volume. Its second result calculates the final concentration from the entered starting volume: C₂ = C₁V₁/V₂. The displayed unit is ng/µL, but the same concentration unit must be used for both concentrations. The same volume unit must likewise be used for both volumes.

Worked Example

With the calculator’s default values, the starting solution is 100 ng/µL, the starting volume is 10 µL, the target concentration is 20 ng/µL, and the final volume is 50 µL.

First, calculate the starting volume required for the target:

V₁ = C₂V₂/C₁ = (20 ng/µL × 50 µL)/(100 ng/µL) = 10 µL.

The result is 10.00 µL of starting solution. Separately, using the entered 10 µL starting volume, the concentration after dilution is:

C₂ = C₁V₁/V₂ = (100 ng/µL × 10 µL)/(50 µL) = 20.00 ng/µL.

Both outputs agree because the default inputs describe a consistent dilution. The starting solution contributes 1,000 ng of solute, and that amount distributed through 50 µL corresponds to 20 ng/µL.

Assumptions

• The solute amount is conserved: there is no degradation, loss, precipitation, or transfer error.
• V₂ means the final total solution volume, not the volume of diluent added.
• Concentrations use the same units, and volumes use the same units.
• The calculator performs arithmetic only; it does not account for measurement uncertainty, mixing quality, or material-specific behavior.

Using C1V1 = C2V2 with ng/µL

For a concentration stated in ng/µL, the equation works directly when both concentrations use ng/µL and both volumes use µL. For example, 15 ng/µL multiplied by 4 µL represents 60 ng of solute. Dividing that amount by a final volume of 12 µL gives 5 ng/µL.

The equation is useful when planning a dilution from a known stock, determining the concentration after combining a measured stock volume with a final solution, or checking whether a proposed dilution is internally consistent. It is not limited to nanograms: it applies to any conserved solute amount when the concentration and volume units are compatible.

1. Identify which value is unknown and rearrange C₁V₁ = C₂V₂ to solve for it.
2. Convert concentrations to the same unit and volumes to the same unit before calculating.
3. Use the intended final total volume for V₂.
4. Check that the calculated amount and concentration are physically consistent with a dilution.

If you need to prepare a final volume of 50 µL and the calculated starting aliquot is 10 µL, the remaining volume is nominally 40 µL of diluent. That subtraction is a volume-planning estimate. In some mixtures, volumes do not add perfectly, and protocols may specify bringing the mixture to a final volume rather than adding an exact diluent volume. Follow the relevant method rather than treating the calculator as a laboratory procedure.

Units, Dilution Factors, and Reading the Result

ng/µL is numerically equivalent to µg/mL: 1 ng/µL = 1 µg/mL. It is also equivalent to 1 mg/L. These equivalences can help when a stock label or protocol uses a different unit, but convert carefully and keep both concentration entries in the same unit. A volume mismatch is equally important: 1 mL = 1,000 µL. If one volume is entered in mL and the other in µL without conversion, the calculated result can be off by a factor of 1,000.

A dilution factor is often defined as final volume divided by starting-solution volume, V₂/V₁. In the example, 50 µL/10 µL = 5, so the starting concentration is reduced fivefold, from 100 to 20 ng/µL. Some laboratories use “1:5 dilution” to mean one part stock in five parts final mixture; others may describe one part stock plus five parts diluent. Because that wording can be ambiguous, use the stated volumes and equation rather than relying on a ratio label alone.

Common Errors and Limits

• Using diluent volume as V₂: V₂ is the final total volume. If 10 µL of stock is mixed with 40 µL of diluent, the nominal final volume is 50 µL, not 40 µL.
• Mixing units: Keep concentration units consistent and volume units consistent. Convert before entering values.
• Confusing the two outputs: “Starting volume needed” answers how much stock is required for the target. “Concentration after dilution” uses the starting volume you entered.
• Rounding too early: Retain extra digits during planning and round only to a volume that can be measured reliably. A displayed decimal does not mean the volume can be measured to that precision.
• Trying to concentrate a sample: If C₂ is greater than C₁ while V₂ is greater than V₁, the simple dilution setup may not be achievable by adding diluent. Concentrating a solution requires a separate process and assumptions.

The equation presumes the solute remains in solution and that the stated concentrations are meaningful for the material and conditions. It does not calculate concentration from absorbance, correct for sample purity, account for degradation, or estimate pipetting uncertainty. For work at the bench, follow your lab method, the safety data sheet (SDS), and your supervisor.

Frequently Asked Questions

How do I calculate V1 from C1, C2, and V2?
Rearrange the dilution equation: V₁ = C₂ × V₂ ÷ C₁. Use matching concentration units and matching volume units.

Is ng/µL the same as µg/mL?
Yes. 1 ng/µL equals 1 µg/mL, because converting nanograms to micrograms and microliters to milliliters applies the same factor of 1,000.

Does V2 mean the amount of water or diluent I add?
No. V₂ is the final total volume of the solution. The diluent amount is often estimated by subtracting the starting aliquot from the intended final volume, but actual preparation methods may specify reaching a final volume.

Can I use C1V1 = C2V2 for any solution?
It applies to straightforward dilution when the solute is conserved and concentrations and volumes are defined consistently. It does not handle reactions, precipitation, losses, concentration processes, or changes in the solute amount.

Why does the calculator give a volume larger than the final volume?
That can occur if the requested target concentration is higher than the stock concentration. The equation then indicates that ordinary dilution cannot meet the target at that final volume; a more concentrated starting material or a separate concentration step would be needed.

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 | ng/µL | 100 | 0
in v1 | Starting volume V1 | µL | 10 | 0
in c2 | Target concentration C2 | ng/µL | 20 | 0
in v2 | Final volume V2 | µL | 50 | 0
out vneeded | Starting volume needed | µL | c2 * v2 / c1 | 2
out cfinal | Concentration after dilution | ng/µL | c1 * v1 / v2 | 2