C1V1 C2V2 Formula for Dilution Calculations

The c1v1 c2v2 formula calculator solves for the missing concentration or volume in a simple dilution, using the relationship between an initial solution and a diluted solution. Enter the two known values and select which quantity is unknown; the result is the fourth value needed to satisfy the equation. Use consistent concentration units and consistent volume units.

Formula

The standard dilution equation is C₁V₁ = C₂V₂. It says that, for a dilution in which no solute is added or removed, the amount of solute before dilution equals the amount after dilution.

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

The calculator solves whichever variable you choose: C₁ = C₂V₂/V₁; V₁ = C₂V₂/C₁; C₂ = C₁V₁/V₂; or V₂ = C₁V₁/C₂. Since the same volume unit appears on both sides, it cancels in the ratio. This example calculator uses nonnegative concentrations and volumes; choose a different appropriate unit consistently if your data are not expressed in mol/L and mL.

Worked Example

The defaults are C₁ = 1 mol/L, V₁ = 10 mL, C₂ = 0.1 mol/L, and V₂ = 100 mL. The selector defaults to solving for C₁. Substituting into the rearranged formula:

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

The millilitre units cancel, and the result is 1 mol/L, matching the calculator’s four-decimal display. A quick check gives C₁V₁ = 1 × 10 = 10 mol·mL/L and C₂V₂ = 0.1 × 100 = 10 mol·mL/L.

Assumptions

The solute is conserved during dilution: none is lost, added by reaction, or precipitated.
The final volume means total solution volume, not the volume of solvent added.
The concentrations and volumes describe the same solute and the same before-and-after preparation.
This is arithmetic for study and lab planning; it does not specify a laboratory procedure.

What the Equation Means

Concentration is amount of solute per volume. Multiplying concentration by volume therefore gives the amount of solute represented by that solution portion. In a dilution, solvent increases the total volume while the solute amount stays the same, so concentration falls. The equation equates the initial and final solute amounts.

For instance, the worked example represents 10 mL of a 1 mol/L stock diluted to a total of 100 mL. Its final concentration is one tenth of the original, 0.1 mol/L. The total volume is ten times larger, so the concentration is ten times smaller. This reciprocal relationship is a useful sanity check: ordinary dilution should not make a solution more concentrated.

When to Use It and How to Read the Result

Use C1V1 = C2V2 when a known solution is diluted and you need to find a starting aliquot, final concentration, or final volume. It is commonly used for classroom problems and routine lab-planning calculations where the initial and target concentrations are known or one is being determined.

To calculate stock volume, enter the stock concentration, desired final concentration, and final total volume; solve for V1.
To find the diluted concentration, enter the starting concentration and volume plus the final volume; solve for C2.
To find how much final solution a given stock portion can produce at a target concentration, solve for V2.
To check a reported dilution, calculate both concentration-volume products; they should agree within the precision of the inputs.

The output uses the unit printed beside the selected variable: mol/L for concentration or mL for volume in this calculator. It is a mathematical result, not an instruction to measure or prepare a solution. Practical work may require tolerances, compatible materials, validated methods, and safety controls. Follow your lab method, the safety data sheet (SDS), and your supervisor.

Common Errors and Limits

The most common mistake is treating V2 as the solvent volume to add. It is the final total solution volume. If a calculation calls for 100 mL final volume, the equation does not mean to add 100 mL of solvent to the stock; the resulting total would be larger than 100 mL.

Mixing units: The two volumes must use the same unit if left as a ratio. Convert before calculating if one is in mL and the other in L. Concentrations must likewise use compatible units.
Rounding too early: Keep extra digits in intermediate calculations and round the reported value to match the precision justified by the measurements.
Using the wrong stock concentration: Confirm that the stated concentration refers to the actual starting solution, not a label or a different dilution stage.
Assuming every mixture is a simple dilution: Reactions, evaporation, changes in volume on mixing, or solute loss can invalidate the conserved-solute assumption.

The relationship is a mass-balance equation, not a guarantee that real volumes add exactly or that a target concentration is experimentally achieved. It does not account for chemical reactions, non-ideal solution behavior, uncertainty, or changes in temperature. If the process changes the solute amount or the relevant final volume, use a model suited to that process instead.

Frequently Asked Questions

What does C1V1 = C2V2 mean?
It states that the amount of solute in the starting portion equals the amount in the final diluted solution, provided no solute is gained or lost.

How do I solve for V1?
Rearrange the equation to V1 = C2V2/C1. Use the target concentration and final total volume, then divide by the starting concentration.

Is V2 the amount of water to add?
No. V2 is the final total volume of the solution. The equation does not directly calculate the volume of solvent to add.

Can I use different volume units?
Convert them to the same unit first, or ensure the calculator’s ratio uses matching units. For example, do not divide a volume in mL by one in L without conversion.

Does the formula work for mixing two stock solutions?
Not by itself in its usual one-stock dilution form. For multiple solutions, account for the solute amount contributed by each and the final total volume, while checking whether reactions or volume changes matter.

Formula used

in c1 | Initial concentration | mol/L | 1 | 0
in v1 | Initial solution volume | mL | 10 | 0
in c2 | Final concentration | mol/L | 0.1 | 0
in v2 | Final solution volume | mL | 100 | 0
sel solve | Solve for | c1=1, v1=2, c2=3, v2=4
out answer | Solved value | selected units | (solve=1)*c2*v2/v1+(solve=2)*c2*v2/c1+(solve=3)*c1*v1/v2+(solve=4)*c1*v1/c2 | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation with the constants and conversion factors written on the page, rounded as each result states. See method and constants, the disclaimer or report an error.