How C1V1 = C2V2 turns a stock solution into a working solution
A stock solution dilution starts with a known initial concentration and a desired final concentration. The amount of solute does not change when an aliquot of the stock is transferred and diluted, so initial concentration multiplied by transferred stock volume equals final concentration multiplied by final volume. This conservation relationship is written as C1V1 = C2V2.
This calculator follows the same workflow as a standard laboratory dilution worksheet. C1 is the concentration of the starting stock, V1 is the stock volume to transfer, C2 is the target working concentration, and V2 is the total final volume after diluent has been added. The calculator solves for V1 because C1, C2, and V2 are the values normally known when preparing a working solution.
Concentration and volume units do not have to match on screen. Each concentration is normalized to mol/L and each volume is normalized to liters for the equation, then the result is converted back to the selected V1 unit. Keeping unit conversion inside the calculation avoids the common thousand-fold errors that occur when mM and µM or mL and µL are mixed manually.
V1 = (C2 × V2) ÷ C1
Worked dilution example: prepare 20 mL of a 50 µM solution
Suppose a laboratory has a 10 mM stock solution and needs 20 mL of a 50 µM working solution. First convert 10 mM to 10,000 µM. Substituting the values into V1 = (C2 × V2) ÷ C1 gives (50 µM × 20 mL) ÷ 10,000 µM = 0.1 mL. That stock volume is also 100 µL.
To reach a final volume of 20 mL, the mathematical diluent amount is 20 mL minus 0.1 mL, or 19.9 mL. The concentration ratio is 10,000 µM divided by 50 µM, so the preparation is a 200-fold dilution. Depending on the protocol, the practical instruction may be to transfer 0.1 mL of stock and bring the solution to a total volume of 20 mL rather than measuring 19.9 mL independently.
- C1: 10 mM stock concentration
- C2: 50 µM final concentration
- V2: 20 mL final solution volume
- V1: 0.1 mL or 100 µL of stock solution
- Dilution factor: 200×
Match concentration and volume units before calculating
Molar concentration units represent powers of ten relative to one mole per liter. One M equals 1,000 mM, one mM equals 1,000 µM, one µM equals 1,000 nM, and the same progression continues through pM and fM. Volume units follow a similar decimal structure: one liter equals 1,000 mL, one mL equals 1,000 µL, and one µL equals 1,000 nL.
The unit labels remain attached to every input and output because a number without its unit is incomplete laboratory information. A result of 0.1 mL and a result of 0.1 µL differ by a factor of one thousand. When documenting a preparation, record the original inputs, selected units, equation, calculated transfer volume, and the precision supported by the actual equipment.
Convert mass concentration and molarity
Choose a direct stock dilution or serial dilution calculator workflow
A valid mathematical dilution requires the final concentration to be lower than the stock concentration. If C2 is equal to or greater than C1, the tool stops and asks for the inputs to be checked. It also accepts only positive numbers. These checks prevent negative diluent volumes but do not establish whether a selected concentration is chemically achievable.
A direct dilution uses the calculated V1 in one transfer and usually involves fewer preparation steps. If V1 is below the reliable range of the available pipette, an intermediate or serial dilution can replace one impractically small transfer with several measurable steps. Each added step must still follow the applicable mixing and handling protocol.
Before preparing a solution, verify the stock label, concentration basis, purity or activity correction, solvent compatibility, final-volume convention, temperature, and appropriate containment. The calculator performs arithmetic only and cannot determine whether a dilution is chemically stable, experimentally suitable, or safe to prepare.
- Use the total final solution volume for V2, not the volume of diluent alone.
- Keep C1 and C2 on the same concentration basis; do not mix molarity with mg/mL.
- Check that the calculated V1 falls within the validated range of the selected pipette.
- Use a serial dilution when a direct transfer volume is too small to measure reliably.
Dilution Calculator questions and answers
How do I use the C1V1 C2V2 dilution calculator?
Enter the stock concentration as C1, the desired final concentration as C2, and the final solution volume as V2. Select the unit beside each value, then calculate. The tool returns V1, the amount of stock solution required, along with the diluent volume and dilution factor.
Can the stock and final concentrations use different units?
Yes. C1 and C2 can independently use fM, pM, nM, µM, mM, or M. The calculator converts both concentrations to mol/L before applying C1V1=C2V2, so values such as 10 mM and 50 µM can be used together.
How is the amount of diluent calculated?
Diluent volume equals the requested final volume minus the calculated stock volume. For example, if V2 is 20 mL and V1 is 0.1 mL, the mathematical diluent volume is 19.9 mL.
What is the dilution factor in a stock solution calculation?
For a simple one-step dilution, the dilution factor is C1 divided by C2, after both concentrations have been converted to the same unit. It is also equivalent to V2 divided by V1.
Does this dilution calculator replace a laboratory protocol?
No. It performs arithmetic only. It cannot assess chemical compatibility, solubility, stability, measurement uncertainty, significant figures, mixing order, temperature effects, or laboratory safety requirements.