Dilution Calculator

Dilution reduces concentration by adding solvent while keeping the same amount of solute. Labs rarely prepare every concentration from solid — a 6 M HCl stock gets pipetted and diluted to working strength. The dilution equation encodes conservation of moles: what you take from the stock equals what ends up in the final flask.

Dilution formula:

C₁V₁ = C₂V₂

Where C₁ is initial concentration, V₁ is volume taken from stock, C₂ is final concentration, and V₂ is final total volume after dilution. Moles before = moles after: n = C₁V₁ = C₂V₂. Solvent to add = V₂ − V₁. Units for C must match (both M, both %, etc.); V units must match (both mL or both L).

Enter any three variables to solve the fourth. Serial dilutions multiply dilution factors: two tenfold steps give 1/100 final concentration. Plating microbiology uses 1:10, 1:100 series; analytical chemistry prepares calibration curves from a single standard.

Worked example: Make 500 mL of 0.200 M NaCl from 2.00 M stock. C₁V₁ = C₂V₂ → V₁ = C₂V₂/C₁ = 0.200 × 500 / 2.00 = 50 mL stock. Pipette 50 mL into a volumetric flask, add water to 500 mL total. Solvent added = 450 mL. A 1:10 dilution of 0.050 M gives C₂ = 0.0050 M regardless of whether you dilute 10 mL to 100 mL or 1 mL to 10 mL.

Use with molarity for concentration definitions, molar mass when starting from solid, and pH when diluting acids or bases (strong acid pH shifts predictably at high dilution). Never add water to concentrated acid — add acid to water with stirring to manage heat.