C1V1 = C2V2 Calculator and Dilution Guide

The C1V1 = C2V2 calculator finds the volume of a concentrated starting solution needed to make a more dilute solution, or calculates another missing value in a dilution. Enter any three of the four quantities—initial concentration (C1), initial volume (V1), final concentration (C2), and final volume (V2)—using consistent concentration and volume units; the calculator returns the missing quantity.

Formula

The dilution equation is C1V1 = C2V2. It expresses conservation of the amount of dissolved substance during dilution: the amount present before adding solvent equals the amount in the final solution, assuming no solute is lost or added.

• C1 is the starting solution concentration, here in mol/L.
• V1 is the volume of starting solution needed, here in mL.
• C2 is the target final concentration, here in mol/L.
• V2 is the target final solution volume, here in mL.

Solving for the starting volume gives V1 = C2 × V2 / C1. The second calculator output estimates the volume of solvent by subtracting V1 from V2. Concentrations must use the same unit as each other, and volumes must use the same unit as each other. Since both volumes in this calculator are in mL, no conversion is needed in the formula. For other unit choices, convert explicitly before calculating.

Worked Example

Using the calculator’s default values, C1 = 1 mol/L, V1 = 10 mL, C2 = 0.1 mol/L, and V2 = 100 mL, calculate the starting volume required for the target:

V1 = C2 × V2 / C1
V1 = 0.1 mol/L × 100 mL / 1 mol/L
V1 = 10 mL

The solvent estimate is 100 mL − 10 mL = 90 mL. The calculated outputs are therefore 10.000 mL of starting solution and 90.000 mL of approximate solvent. The concentration units cancel, leaving a volume. This example also checks the original relationship: 1 mol/L × 10 mL = 0.1 mol/L × 100 mL.

Assumptions

• The solute is conserved during dilution: there is no reaction, precipitation, evaporation, or transfer loss.
• The starting and target concentrations describe the same dissolved substance and use matching units.
• The target volume is the final solution volume, not necessarily the volume of solvent added.
• The solvent estimate assumes volumes are additive. Real mixtures can change volume slightly when combined.

When to Use C1V1 = C2V2

This equation is useful for planning a simple dilution when a stock solution’s concentration is known and a lower concentration is needed at a specified final volume. It applies to many routine aqueous solution calculations, provided the substance remains dissolved and chemically unchanged. It can also be rearranged to find a target concentration, stock concentration, or final volume when the other three quantities are known.

For example, if a 1 mol/L stock is used to prepare 100 mL at 0.1 mol/L, the calculation gives 10 mL of stock. The remaining volume is not automatically 90 mL of solvent in an exact volumetric preparation: the usual interpretation is to add solvent until the total solution reaches 100 mL. That distinction matters because mixing can cause slight volume changes.

The calculator presents V1 as its headline answer because the common dilution-planning question is how much stock to measure. Its fields show example values, but the equation itself is symmetric: enter the relevant known quantities and rearrange for the one unknown. Do not treat all four defaults as simultaneously fixed when asking for a different unknown; use the formula directly or a calculator configuration that selects the intended missing variable.

Reading Results and Choosing Units

Concentration units must match: mol/L with mol/L, mg/mL with mg/mL, or another consistent pair. If the stock concentration is in mol/L and the target is in mmol/L, convert one first; 1 mol/L equals 1000 mmol/L. Volume units should also match. For instance, if one volume is in liters and the other in milliliters, convert one before applying the equation. The calculator’s volume inputs are both mL.

A result of 10 mL means the calculated aliquot of stock, not the volume of solvent. For a practical preparation, transfer the stock aliquot and bring the mixture to the specified final volume, following the validated method for the work. The solvent output is only a simple estimate of the difference between final volume and stock volume; it should not override a method that specifies “dilute to volume.”

Values are displayed to three decimal places, which is a formatting choice rather than a claim of measurement accuracy. Use significant figures appropriate to the concentration data, volumetric equipment, and required precision. If an input is uncertain, reporting many decimal places does not make the result more certain.

Limits and Common Mistakes

• Using solvent volume instead of final volume: C2 refers to the concentration after dilution, and V2 is the total final solution volume. Adding a calculated amount of solvent to the stock may not produce exactly that final volume.
• Mixing units: A calculation using 0.1 mol/L and 100 mL is consistent with an answer in mL. Mixing mol/L with mmol/L without converting produces a result wrong by a factor of 1000.
• Applying it to a reaction: C1V1 = C2V2 assumes the dissolved amount is conserved. It does not account for chemical consumption, binding, precipitation, degradation, or a change in the species being measured.
• Using an unsuitable stock: The equation does not determine whether a stock is stable, compatible, sufficiently concentrated, or appropriate for a particular method. Those questions require substance- and method-specific information.

The equation is a mass-balance calculation, not a complete preparation protocol. It does not correct for non-ideal behavior, temperature-dependent volume, solvent compatibility, or measurement uncertainty. Where bench work is implied, follow your lab method, the safety data sheet (SDS), and your supervisor.

Frequently Asked Questions

What does C1V1 = C2V2 mean?
It states that the amount of solute in the measured stock aliquot equals the amount in the final diluted solution, assuming the solute is conserved.

How do I calculate V1?
Rearrange the equation to V1 = C2 × V2 / C1. Keep the concentration units consistent and use matching volume units.

Does V2 mean the amount of water to add?
No. V2 is the final total solution volume. The solvent amount may be approximately V2 − V1, but volumetric preparation generally means adding solvent until the mixture reaches V2.

Can I use C1V1 = C2V2 with different concentration units?
Convert them to the same unit first. For example, convert mmol/L to mol/L or convert mol/L to mmol/L before substituting values.

Can the equation calculate a dilution series?
It can calculate each individual dilution step, but each step needs its own starting concentration, transferred volume, and final volume. A stepwise series should account for the actual concentration produced at the preceding step.

Why is the solvent estimate not always exact?
Solution volumes may not add perfectly, and the equation describes conserved solute rather than the physical volume change on mixing. For a specified final volume, bring the solution to that volume rather than relying on a subtraction alone.

Related

• Sample Dilution Factor Calculator and Formula
• Dilution Formula Calculator: C1V1 = C2V2 for Molarity
• Dilution Factor Calculator: Final Molarity From Volumes

in c1 | Initial concentration C1 | mol/L | 1 | 0
in v1 | Initial solution volume V1 | mL | 10 | 0
in c2 | Final concentration C2 | mol/L | 0.1 | 0
in v2 | Final solution volume V2 | mL | 100 | 0
out v1calc | Required initial volume V1 | mL | c2 * v2 / c1 | 3
out solvent | Approximate solvent volume to add | mL | v2 - v1calc | 3