C1V1 = C2V2 Dilution Calculator
Find the volume of stock solution needed for a dilution. Enter the stock concentration, desired concentration, and desired final volume.
Find Stock Solution Volume
C1V1 = C2V2 Dilution Formula
Where:
- \(C_1\) — concentration of the stock solution
- \(V_1\) — volume of stock solution needed
- \(C_2\) — desired concentration of the final solution
- \(V_2\) — desired final volume of the diluted solution
The equation states that the amount of dissolved substance taken from the stock equals the amount in the final solution. Use compatible concentration units for \(C_1\) and \(C_2\), and consistent volume units for \(V_1\) and \(V_2\).
C1V1 = C2V2 – Calculation Example
Example: You have a 1 mol/L stock solution and want 1 L of a 0.1 mol/L solution. Leave Stock Concentration (C1) and Desired Volume (V2) at their defaults, and change Desired Concentration (C2) to 0.1 mol/L.
\[V_1=\frac{C_2V_2}{C_1}=\frac{(0.1\,\mathrm{mol/L})(1\,\mathrm{L})}{1\,\mathrm{mol/L}}=0.1\,\mathrm{L}\]
Result: Use 0.1 L (100 mL) of stock solution, then add diluent until the total volume is 1 L.
How to use the calculator
- Enter the concentration of the solution you are diluting in Stock Concentration (C1) and select its Units.
- Enter the concentration you want in Desired Concentration (C2) and select its Units. The desired concentration must be lower than the stock concentration after any valid unit conversion.
- Enter the final amount of solution to prepare in Desired Volume (V2) and select L or mL under Units.
- Read Required Volume (V1) as the amount of stock to measure. If you selected mL for Desired Volume (V2), read the output warning below before using the number.
The default concentrations are both 1 mol/L. Because they are equal, the calculator displays an error until you enter a lower Desired Concentration (C2), such as 0.1 mol/L.
What C1V1 = C2V2 means
Dilution lowers a solution’s concentration by adding solvent, also called diluent. The amount of dissolved substance stays the same: the portion measured from the stock contains the same amount that ends up in the prepared solution. That conservation is what \(C_1V_1=C_2V_2\) expresses.
The calculated \(V_1\) is the volume of stock solution, not the volume of diluent to add. For the example above, measure 100 mL of stock and bring the solution to a final volume of 1 L. Do not simply add 1 L of diluent: doing so would produce more than 1 L of solution and a lower concentration than intended.
The ratio \(C_2/C_1\) is the fraction of the final volume that comes from the stock. For a tenfold dilution, \(C_2/C_1=0.1\), so the stock occupies one-tenth of the final volume. This makes the result easy to check: when the desired concentration is lower than the stock concentration, \(V_1\) should be smaller than \(V_2\).
Units, output warning, and practical limits
Important mL output warning: The calculator converts Desired Volume (V2) to liters for its calculation, but labels the resulting number with the unit you selected for V2. When you select mL, the displayed number is therefore in liters despite its mL label. Multiply that number by 1,000 to obtain the required stock volume in mL. For example, with 1 mol/L stock, 0.1 mol/L desired concentration, and 100 mL desired volume, the output displays “0.01 mL”; the correct required volume is 0.01 L, or 10 mL. Selecting L for Desired Volume (V2) avoids this labeling issue.
Use concentration units that describe the same kind of quantity. The calculator converts mM to mol/L correctly, so those two units can be used together. It does not use a substance’s molar mass when handling g/L: although it accepts a mix of g/L and mol/L or mM, that mix does not yield a valid conversion. Use g/L for both concentrations, or use mol/L and mM as appropriate. Converting g/L to mol/L requires the solute’s molar mass.
Enter positive concentrations and a positive final volume. This equation assumes the dissolved substance is conserved during preparation; it does not account for reactions, losses, or changes in concentration after mixing. For accurate work, measure the stock with suitable equipment and bring the mixture to its specified final volume. If you are preparing an acetate solution whose pH also matters, the acetate buffer composition calculator addresses the buffer components. For measurements that relate absorbance to concentration, see the Beer–Lambert law calculator.
Frequently Asked Questions
How do I calculate a dilution by hand?
Divide the target concentration by the stock concentration, then multiply by the desired final volume. For example, to make 40 mL at 25 mM from a 250 mM stock, calculate \(V_1=(25/250)\times40=4\) mL of stock. Measure the stock, then add diluent until the total volume reaches 40 mL.
What is a dilution factor, and what does 1:10 mean?
The dilution factor is the stock concentration divided by the final concentration: \(C_1/C_2\). A factor of 10 means the final concentration is one-tenth of the stock concentration. The notation “1:10” can be ambiguous: it may mean one part stock in ten parts total or one part stock plus ten parts diluent. State the volumes explicitly when accuracy matters.
How do I calculate a serial dilution?
Multiply the dilution factors of the individual steps to find the overall factor. Two successive tenfold dilutions produce a hundredfold dilution. For each step, calculate the stock volume using that step’s starting concentration, target concentration, and final volume. Mix thoroughly before taking the portion for the next step; otherwise, its actual concentration may differ from the calculated value.
Can I convert between g/L and mol/L for a dilution?
Yes, if you know the solute’s molar mass. Divide a concentration in g/L by the molar mass in g/mol to get mol/L; multiply mol/L by the molar mass to get g/L. For example, a 10 g/L solution of a substance with a molar mass of 100 g/mol is 0.1 mol/L. Convert first rather than mixing these unit types in this calculator.
Can dilution produce a higher concentration or a zero-concentration solution?
Adding diluent cannot make a solution more concentrated. To reach a concentration above the stock’s, you need a stronger stock or another preparation method. A target concentration of zero requires no stock at all—only the diluent—and is not a useful application of the dilution equation. This calculator is intended for positive target concentrations below the stock concentration.
Does the equation work when I mix two solutions that both contain solute?
Not in its simple dilution form, which treats the added diluent as containing none of the solute. For two solutions of the same nonreacting solute, add their solute amounts: \(C_aV_a+C_bV_b=C_fV_f\). Use the actual final volume for \(V_f\); it may not equal \(V_a+V_b\) for every mixture.
Is there a normal or recommended dilution ratio?
No single ratio is normal: the appropriate concentration depends on the experiment, assay, or product instructions. Choose a target within the usable range of your method, and check that the required stock volume can be measured accurately with your equipment. For laboratory chemicals or medical preparations, follow the relevant protocol and safety guidance rather than relying on a calculated ratio alone.