Dilution Calculator: C1V1 = C2V2 Explained

A dilution calculator using C1V1 = C2V2 finds the volume of a concentrated starting solution needed to prepare a chosen volume at a lower concentration. Enter the stock concentration, target concentration, and final volume; it returns the stock volume and how much diluent to add.

Formula

The dilution relationship is C1V1 = C2V2. Rearranging it gives V1 = (C2 × V2) / C1, the volume of stock solution to measure. If the final volume is made up by adding diluent, its volume is V2 − V1.

• C1 is the stock (starting) concentration.
• V1 is the volume of stock solution required, in mL in this calculator.
• C2 is the desired final concentration.
• V2 is the desired final solution volume, in mL.

The two concentrations must use the same units, such as both g/L or both percent by volume. The volumes V1 and V2 must use the same volume unit. Concentrations can be expressed in different compatible units only after conversion; for example, convert mg/mL to g/L before using the equation.

Worked Example

Using the calculator’s defaults, prepare 100 mL of a 10-concentration solution from stock at concentration 100. The concentration units cancel because both entries use the same unit.

1. Start with C1V1 = C2V2.
2. Substitute the values: 100 × V1 = 10 × 100 mL.
3. Divide by 100: V1 = (10 × 100) / 100 = 10 mL of stock.
4. Find the remaining volume: 100 mL − 10 mL = 90 mL of diluent.

The calculator therefore returns 10.00 mL of stock and 90.00 mL of diluent. In careful laboratory practice, the final solution is often brought to a total volume of 100 mL rather than assuming that separately measured liquids combine to exactly that volume.

What C1V1 = C2V2 Means

Dilution lowers concentration by spreading a fixed amount of dissolved substance through a larger total volume. The amount of solute taken from the stock is the same amount present in the diluted solution, assuming no material is lost or added through a chemical reaction. Concentration multiplied by volume represents that amount, which is why C1V1 equals C2V2.

For example, if you take 10 mL of a stock solution at 100 units per mL, it contains 1,000 units of solute. Bringing that sample to a final volume of 100 mL gives 10 units per mL. Adding 90 mL of diluent is one way to reach that total volume, but “dilute to 100 mL” is the more precise instruction when volume changes on mixing matter.

How to Use the Calculator

1. Enter the concentration of the stock solution as C1.
2. Enter the desired final concentration as C2, using the same concentration units.
3. Enter the total final volume as V2.
4. Measure the calculated stock volume. Add diluent until the mixture reaches V2, or use the calculated diluent volume when simple volume addition is appropriate.

The result is meaningful for an ordinary dilution when the target concentration is no greater than the stock concentration and the stock volume does not exceed the intended final volume. If C2 is greater than C1, the equation asks for more stock than the final volume; that is not a dilution. A more concentrated source or a different preparation method is needed.

Units, Ratios, and Serial Dilutions

Common concentration units include mol/L (M), mmol/L, g/L, mg/mL, and percentages. A percentage may mean mass per volume, volume per volume, or mass per mass; identify which definition applies before comparing or converting values. Do not enter “10%” as 10 in one field and “0.1” as a fraction in the other without converting them to a consistent scale.

The equation also describes dilution factors. If stock at 100 units per mL is diluted to 10 units per mL, the final concentration is one tenth of the starting concentration: a 1:10 concentration ratio. In a common lab convention, “1:10 dilution” means one part sample brought to ten parts total, so it uses one part sample plus nine parts diluent. Because conventions can differ, write out the actual volumes when precision matters.

For a target too dilute to measure accurately in one step, a serial dilution can be easier. Each step dilutes the previous solution by a known factor; the overall factor is the product of the step factors. For instance, two successive tenfold dilutions produce a thousandfold overall dilution. Calculate each transfer separately and label intermediate containers clearly.

Common Errors and Limits

• Mixing units: Convert concentrations to the same unit and volumes to the same unit before calculating.
• Confusing added volume with final volume: V2 means the total solution volume, not the amount of water or other diluent.
• Rounding too early: Keep extra digits while calculating, then round the measured volume to a practical precision supported by the equipment.
• Assuming perfect measurements: The equation does not account for instrument uncertainty, evaporation, temperature effects, or volume contraction when liquids mix.
• Using an unsuitable concentration definition: Percent by mass cannot automatically be treated as percent by volume.

The formula is a conservation calculation, not a guarantee that a mixture is chemically stable, safe, or appropriate for a particular use. Follow the relevant product instructions and laboratory procedures, and use suitable measurement equipment. This calculator does not determine compatibility or account for reactions between the stock and diluent.

Frequently Asked Questions

What does C1V1 = C2V2 calculate?
It calculates the stock volume V1 needed to make a chosen final volume V2 at a target concentration C2, starting from concentration C1.

How do I calculate how much water to add?
When simple volume addition applies, subtract the stock volume from the final volume: diluent = V2 − V1. For greater accuracy, add diluent until the mixture reaches the specified final volume.

Can I use different units for C1 and C2?
Not directly. Convert them to the same concentration unit first. The equation also requires V1 and V2 to use the same volume unit.

What if the target concentration is higher than the stock concentration?
That is not a dilution. The calculated stock volume would exceed the desired final volume, so use a more concentrated stock or another preparation approach.

Does a 1:10 dilution mean one part stock plus ten parts water?
Usually, a tenfold dilution means one part stock in ten parts total—one part stock plus nine parts diluent. Since notation varies, confirm the intended convention and state the volumes explicitly.

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in c1 | Stock concentration | - | 100 | 0
in c2 | Target concentration | - | 10 | 0
in v2 | Final volume | mL | 100 | 0
out v1 | Stock volume needed | mL | c2 * v2 / c1 | 2
out diluent | Diluent to add | mL | v2 - v1 | 2