Dilution Formula Calculator: C1V1 = C2V2

A dilution formula calculator uses the starting concentration and volume to work out how much stock solution is needed to make a target concentration and final volume. Enter those three values and it returns the stock volume; it also calculates how much diluent to add.

Formula

The standard dilution equation is C₁V₁ = C₂V₂. Rearranged to find the amount of stock solution, it is V₁ = (C₂ × V₂) ÷ C₁. The calculator then finds the diluent volume by subtracting the stock volume from the desired final volume.

• C₁ is the starting, or stock, concentration, in milligrams per milliliter (mg/mL).
• V₁ is the volume of stock solution required, in milliliters (mL).
• C₂ is the desired final concentration, in mg/mL.
• V₂ is the desired final solution volume, in mL.
• V₂ − V₁ is the calculated volume of diluent to add, in mL.

Concentration units for C₁ and C₂ must match, and volume units for V₁ and V₂ must match. The formula expresses conservation of the amount of dissolved substance: dilution changes the concentration by adding solvent, not by changing the amount of solute already present.

Worked Example

Using the calculator’s default values: C₁ = 100 mg/mL, C₂ = 10 mg/mL, and V₂ = 100 mL.

1. Calculate the stock volume: V₁ = (10 mg/mL × 100 mL) ÷ 100 mg/mL = 10 mL.
2. Calculate the diluent volume: 100 mL − 10 mL = 90 mL.
3. Check the result: 100 mg/mL × 10 mL = 1,000 mg of solute; 1,000 mg ÷ 100 mL = 10 mg/mL.

The result is 10.00 mL of stock solution and 90.00 mL of diluent, for 100 mL total at 10 mg/mL. In practice, the final volume should be measured as the total solution volume; adding 90 mL of diluent to 10 mL of stock may not produce precisely 100 mL if volumes do not combine additively.

How to Use a Dilution Calculator

1. Find the stock concentration on the solution label or from a reliable preparation record.
2. Choose the target concentration and the final volume you need.
3. Enter concentrations in the same units and volumes in the same units.
4. Read the stock volume, then use the diluent result as a planning estimate. For a precise final volume, add some diluent, mix, and bring the solution up to the intended final volume using an appropriate calibrated vessel.

For example, a stock concentration of 2 g/L and a target of 200 mg/L cannot be entered as written unless the units are reconciled. Since 2 g/L equals 2,000 mg/L, the target is one tenth of the stock concentration. Keep the volumes in liters or convert both to milliliters; either approach gives the same dilution ratio.

When the Formula Applies

C₁V₁ = C₂V₂ is useful when a known stock solution is diluted to a lower concentration, such as in laboratory solution preparation, classroom chemistry, or other measured mixtures. It assumes that the stock concentration is known, the relevant substance is conserved during mixing, and the target concentration refers to the final, mixed solution.

A dilution cannot make the target concentration greater than the stock concentration using only that stock and a diluent. If C₂ is greater than C₁, the calculated V₁ will exceed V₂, signaling that the requested mixture cannot be made by dilution alone. A more concentrated source or a different preparation method is needed.

The equation is also used for serial dilutions, but each step has its own starting and target concentrations. Calculate each step from the concentration entering that step, not from the original stock unless that is what is actually being used.

Common Errors and Limitations

• Mixing units: Do not compare mg/mL directly with g/L without converting. A factor of 1,000 can produce a serious calculation error.
• Confusing added volume with final volume: V₂ means the total final solution volume, not the volume of diluent alone.
• Rounding too early: Keep extra digits during intermediate calculations and round the measured amount to match the equipment’s precision.
• Assuming exact volumes add: Mixing can change the combined volume. When final concentration matters, prepare to a final volume rather than relying solely on adding two separately measured volumes.
• Ignoring measurement uncertainty: The result is only as dependable as the concentration value and volume measurements entered.

The calculator handles the arithmetic; it does not verify that a stock label is correct, account for chemical reactions, or determine whether a particular solvent is compatible. It is not a substitute for a validated procedure where composition, purity, temperature, or safety requirements matter.

Frequently Asked Questions

What is the dilution formula?
C₁V₁ = C₂V₂, where C₁ and V₁ describe the stock portion, while C₂ and V₂ describe the desired final solution. Rearranging gives V₁ = C₂V₂/C₁.

How do I calculate how much diluent to add?
For a simple volume calculation, subtract the stock volume from the final volume: diluent = V₂ − V₁. For better control of the final concentration, add diluent until the mixture reaches the specified final volume.

Can I use different concentration units?
Yes, but convert them so C₁ and C₂ use the same unit before calculating. For instance, convert both to mg/mL or both to g/L. The volume units must also be consistent.

What if the target concentration is higher than the stock?
Adding diluent can only lower concentration. If the target exceeds the stock concentration, this equation will require more stock volume than the target final volume, which indicates the requested dilution is not possible as stated.

Does the formula work for serial dilutions?
Yes. Apply it separately at each stage using the concentration of the solution being diluted at that stage, the next target concentration, and the chosen final volume.

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