Molarity and Dilution Calculator
Calculate the final molarity after diluting a stock solution by entering initial molarity, initial and final volumes, and a solvent type factor. Perfect for preparing working solutions in the lab.
About this calculator
The dilution equation is derived from conservation of moles of solute: moles before = moles after. Standard form is M1 × V1 = M2 × V2. This calculator extends that relationship with a solvent correction factor S, giving M2 = (M1 × V1 × S) / V2. The solvent factor accounts for non-ideal behaviour when the diluent is not pure water — for example, organic solvents with different densities or solvation properties can alter the effective molarity. When diluting in pure water, set S = 1 to recover the classic formula. Molarity itself is defined as moles of solute divided by liters of solution (n / V), making it the most common concentration unit in quantitative analytical and synthetic chemistry.
How to use
You have a 10 M HCl stock solution. You take V1 = 50 mL and dilute to V2 = 500 mL in pure water (S = 1.0). Using M2 = (M1 × V1 × S) / V2: M2 = (10 × 50 × 1.0) / 500 = 500 / 500 = 1.0 M. Enter M1 = 10, V1 = 50, V2 = 500, solvent factor = 1 and the calculator returns 1.0 M — a standard 1-in-10 dilution. For a non-aqueous solvent with factor 0.95, the result would be (10 × 50 × 0.95) / 500 = 0.95 M.
Frequently asked questions
What is the standard dilution formula M1V1 equals M2V2 and when does it apply?
M1V1 = M2V2 states that the number of moles of solute before dilution equals the number after: molarity times volume is constant. It applies whenever the solvent added is ideal (pure water, density-matched, no reaction with solute) and the volumes are additive. The formula is the starting point for all serial dilution calculations in microbiology, pharmacology, and analytical chemistry. Deviations occur with concentrated acids or highly ionic solutions where volume contraction on mixing makes the final volume slightly less than V1 + added solvent.
How do I account for solvent type when diluting with organic solvents?
When the diluent is an organic solvent like ethanol, DMSO, or acetonitrile, the density and solvation properties differ from water, potentially affecting the effective molarity or solubility of the solute. The solvent correction factor S in this calculator allows you to scale the result accordingly. In practice, you can determine S from density tables or empirical solubility data. For most aqueous dilutions in a general chemistry or biology lab, S = 1 is appropriate.
How many significant figures should I use when reporting diluted molarity values?
Report your final molarity to the same number of significant figures as your least precise input. Volumetric glassware (Class A burettes, pipettes) is typically accurate to 3–4 significant figures, while graduated cylinders give only 2–3. If your stock solution molarity is known to ±0.5%, carry three significant figures throughout. Avoid false precision — writing 1.0000 M when your volumes were measured to ±1 mL in 100 mL (1% error) implies more certainty than the experiment warrants.