Dilution Calculator

At a glance:Dilution is the operation of adding solvent (usually water) to a concentrated stock solution to lower its concentration and increase its volume; it is the most basic step in preparing standards, buffers and reagents in the lab. The core of dilution is 'conservation of solute': you only add solvent, never solute, so the total moles (or mass) of solute are unchanged before and after dilution — only spread over a larger volume, so the concentration falls. Written as a formula this is the famous C₁·V₁ = C₂·V₂, where C₁, V₁ are the concentration and volume before dilution (stock) and C₂, V₂ after dilution (target solution). On both sides C×V represents 'amount of solute' because concentration times volume cancels the volume unit and yields amount. The most common practical question: you have stock at concentration C₁ and want to prepare a solution of concentration C₂ and volume V₂ — how much stock do you take? Rearranging gives V₁ = C₂·V₂ / C₁, which is the 'required stock volume' this calculator returns. After taking the stock, add solvent up to V₂; the solvent (water) volume to add = V₂ − V₁. The 'dilution factor' = C₁ / C₂ = V₂ / V₁ represents how many times the solution is diluted; for example diluting 2 M to 0.5 M is a 4-fold dilution (written 1:4, i.e. 1 part stock to 4 parts solution). Using this tool's default: stock C₁ = 2 M, want V₂ = 100 mL of C₂ = 0.5 M, take V₁ = 0.5 × 100 / 2 = 25 mL, then add 100 − 25 = 75 mL water, dilution factor = 2 / 0.5 = 4. Notes on using the dilution formula: first, the units of C₁ and C₂ must be consistent (both mol/L, or both %, mg/mL), and V₁ and V₂ must share a volume unit; the formula does not restrict the unit type, only that both sides use the same kind and unit. Second, the target concentration C₂ cannot exceed the stock C₁ — adding solvent alone cannot make a solution more concentrated; if C₂ > C₁ you need a more concentrated stock or evaporation, and this calculator will flag that dilution is impossible. Third, the correct practice is 'take stock first, then add solvent to the mark', not measure water first then add stock, because the dissolved solute also occupies volume; especially when diluting concentrated acids or bases, always add acid to water to avoid violent exothermic splashing. Fourth, the formula assumes additive volumes and a non-reacting solute; for highly concentrated solutions with noticeable volume contraction (e.g. concentrated sulphuric acid) it is only approximate. Dilution is the basis of serial dilution and molarity conversion: a serial dilution repeatedly applies C₁V₁=C₂V₂ to make a concentration gradient, used in microbiology counting and standard-curve preparation. In short, the dilution calculator quantifies 'how much stock, how much water' into a single step — a daily tool in chemistry, biology, medical laboratory and pharmacy preparation.