Concentration of the concentrated stock solution
Volume to take from the stock solution
Target concentration after dilution
≈ 1 part stock + 1.5 parts solvent
250
mL150
mL — concentration and volume of the stock solution.
— concentration and volume of the final diluted solution.
Algebraic rearrangement of the dilution law to isolate the variable you are solving for ().
Dimensionless ratio telling you how many times the original concentration has been diluted. It also reads as a 1 : (DF − 1) ratio — 1 part stock per (DF − 1) parts solvent —, as shown under the result. It is the basis for planning serial dilutions in microbiology and biochemistry.
Diluting means adding solvent without touching the solute: the amount of solute (moles or mass) stays constant (). Since that amount is concentration times volume (), equating «before» and «after» gives directly. The whole calculator is, at heart, this single mass balance.
On paper, the solvent to add is . But at the bench volumes of real mixtures are rarely additive, because of intermolecular interactions (hydrogen bonding, for instance). Mixing 50 mL of ethanol with 50 mL of water yields ~96 mL, not 100 mL, due to the contraction of partial molar volumes.
Diluting highly concentrated solutions —especially strong acids and bases— is not thermally neutral: ion hydration releases a large amount of heat. To prevent splashing from localized boiling, the golden rule is to always add the concentrated reagent slowly to the solvent, never the reverse («acid to water»).
only describes adding solvent: concentration drops, volume rises. If the inputs imply or , the process is no longer a dilution but a concentration, which requires evaporating solvent, adding pure solute, or precipitation — and obeys a different mass balance. The calculator flags this with a warning when the values cross that boundary. To prepare a solution from a concentrated commercial reagent, use the Commercial Solutions & Reagents calculator.