Solve a stock solution dilution with C1V1 = C2V2
A solution dilution calculator finds one missing value among stock concentration C1, stock volume V1, final concentration C2, and final solution volume V2. Select the unknown and enter the other three quantities. This four-way layout supports both forward preparation questions and reverse homework checks without changing the underlying mass-balance relationship.
The calculator is intended for a solute that remains chemically unchanged while a stock solution is diluted. It keeps concentration units paired and volume units paired, so mol/L may be used for both concentrations while millilitres are used for both volumes. The reported answer retains the selected unit and identifies whether it is a concentration, an aliquot of stock, or a final prepared volume.
Understand what each dilution variable means
The equation C1V1 = C2V2 says that the proportional amount of solute taken from the stock equals the amount present in the final diluted solution. C1 describes the original stock, V1 is the stock aliquot used, C2 is the desired concentration after dilution, and V2 is the total volume of the finished solution. The calculator rearranges this equation for whichever one of those four values is missing.
Final volume V2 is not the same quantity as solvent volume added. When V2 is at least V1, the simple difference V2 − V1 is shown as an estimate of solvent needed to reach the final volume. In careful volumetric work, transfer the stock aliquot and bring the mixture to the final mark; do not automatically pour in exactly that difference, because contraction, expansion, dissolved material, and transfer conditions can make volumes non-additive.
Follow a solution dilution example
To prepare 250 mL of 0.100 mol/L solution from a 1.00 mol/L stock, calculate V1 = C2V2 ÷ C1. Substitution gives V1 = 0.100 × 250 ÷ 1.00 = 25.0 mL. The simple solvent-volume estimate is 250 − 25 = 225 mL, while the practical instruction for accurate work is to dilute the 25.0 mL aliquot to a final total volume of 250 mL.
The same equation can recover the final concentration: if 15 mL of 2.0 mg/mL stock is brought to 60 mL, C2 = 2.0 × 15 ÷ 60 = 0.50 mg/mL. Concentration units must match each other before entry. Volume units may be mL, L, or another shared unit because their common conversion cancels, but mixing 25 mL with a V2 entered as 0.250 without converting both creates a thousandfold error.
Check the direction and physical meaning of the result
Multiply C1 by V1 and C2 by V2 using the displayed values. The products should agree within rounding. For an ordinary dilution, C2 should not exceed C1 and V2 should not be smaller than V1. If either condition fails, the scenario describes concentration, evaporation, reaction, or an input-role error rather than simply adding solvent, so review the problem before acting on the number.
Carry enough significant digits through the calculation and round the final result to match the least precise measured input. A mathematically valid stock aliquot may still be too small for available equipment. If the aliquot falls below a pipette’s reliable range, use a suitable intermediate dilution or a different preparation scale instead of treating screen precision as measurement accuracy.
Preparation limits, safety, and private use
This calculator does not account for purity, assay, hydration state, density, reaction stoichiometry, temperature-dependent volume, activity, or solute instability. It does not provide an instruction to mix unfamiliar chemicals. Verify chemical identity, compatibility, mixing order, protective equipment, ventilation, container, storage, and disposal with an approved procedure. Medical, pharmaceutical, biological, and regulated preparations require their current validated instructions.
The values are calculated in the current browser tab. NexaCurrent does not upload the quantities, formulas, chemical names, element choices, or other information entered here, and no account is needed. Copying is a deliberate action after the answer and working are visible. Refreshing or leaving the page clears the current calculation, so keep a copied result if it is needed for later study.