The dilution equation: C1V1 = C2V2
A dilution changes concentration by increasing the solution volume while keeping the amount of solute constant. Let C₁ be the stock concentration, V₁ the stock volume you take, C₂ the target concentration and V₂ the final solution volume. Rearranging C₁V₁ = C₂V₂ gives V₁ = C₂V₂ / C₁.
Enter the three known quantities above. The calculator converts compatible concentration and volume units, gives the stock volume, and displays the nominal difference between final and stock volumes. It also shows the dilution factor, defined here as stock concentration divided by target concentration. A 100-fold dilution has one part stock in 100 parts final solution.
Worked example: 10 mM stock to 100 µM
Suppose you need 1 mL of a 100 µM solution from a 10 mM stock. First express both concentrations in the same units: 10 mM is 10,000 µM. The dilution factor is 10,000 / 100 = 100. The required stock volume is therefore 1 mL / 100 = 10 µL.
Bring that stock aliquot to a final volume of 1 mL. If the volumes are additive, the nominal diluent volume is 990 µL. A preparation requiring accurate final volume should follow the appropriate volumetric method rather than assuming all liquid volumes add exactly.
Compatible units, without hidden conversions
M, mM, µM and nM describe molar concentration. The calculator also accepts mg/mL, µg/mL and ng/µL as mass-per-volume units. For example, 1 ng/µL equals 1 µg/mL. Stock and target must both belong to the same concentration family.
Converting a mass concentration to molarity requires the solute's molar mass. This tool refuses to make that conversion implicitly. Use the molarity calculator when starting from a mass and molecular-weight value. Percentage, activity and optical-density units are not included here.
When a single dilution is not enough
The target cannot be more concentrated than the stock. Equal concentrations need no dilution. Very small calculated aliquots may be difficult to measure with your equipment; an intermediate stock can make the preparation more practical. For a repeated dilution series, use the serial dilution calculator. It shows each transfer and the volume left in every tube. This page calculates a single stock-to-target step; neither tool estimates a pipette's accuracy.
The underlying solute-conservation relation is covered in OpenStax Chemistry 2e. The equation assumes no solute loss or chemical reaction. Save calculation records the entered units and current result for your own notes.