Dilution Equation

The dilution factor DF = C₁/C₂ = V₂/V₁ is a single number (e.g., 10 for a tenfold dilution). The dilution ratio is often written as "1:9" meaning 1 part stock plus 9 parts solvent, giving a total of 10 parts and a dilution factor of 10. This notation is ambiguous in practice: some authors write "1:10" to mean 1 part + 10 parts (DF = 11) and others to mean 1 part in 10 total (DF = 10). To avoid confusion, use the dilution factor DF and calculate V_solvent = V₂ − V₁ directly. In this calculator, we report DF and the solvent volume explicitly.

Yes. The dilution equation works for any concentration unit because it is based on conservation of solute mass or moles. If you use mass concentration (g/L, mg/mL, %), C·V is proportional to the mass of solute, which is conserved. If you use molar concentration (M, mM), C·V is proportional to moles of solute, also conserved. Just make sure C₁ and C₂ use the same unit. Mass concentration is common in pharmaceutical, food, and environmental work where the molar mass of the solute may be unknown or unimportant.

A serial dilution is a sequence of dilutions, where each step uses the output of the previous step as the input stock. The overall dilution factor is the product of the individual factors: 10× × 10× × 10× = 1000×. Serial dilution is used because it is much more accurate than trying to make a 1,000,000× dilution in one step — you would need to pipette 1 µL of stock into 1 L of solvent, which is difficult to do precisely. Instead, three sequential 100× dilutions are easy and precise. Serial dilution is standard in microbiology (for CFU counts), immunology (for antibody titers), and pharmacology (for dose-response curves).

The dilution equation works well for dilute aqueous solutions but becomes less accurate for very concentrated solutions (above 1 M) due to volume contraction and non-ideal mixing. For example, mixing 50 mL of water with 50 mL of ethanol gives about 96 mL, not 100 mL, because the molecules pack more efficiently together. For precise work with concentrated acids and bases, use the density and mass fraction of the stock solution to calculate the required volume. For most lab dilutions (final concentration below 1 M), the error from ignoring volume contraction is under 1%, which is acceptable for routine work.

That is not a dilution — it is a concentration step. The dilution equation C₁V₁ = C₂V₂ with C₂ > C₁ would give V₂ < V₁, meaning the final volume is smaller than the stock volume. Physically this means you would need to remove solvent (by evaporation, lyophilization, or reverse osmosis) or add more solute. The dilution equation assumes you are adding solvent, so C₂ < C₁ and V₂ > V₁ always. If you need a more concentrated solution, start with a more concentrated stock or perform an evaporation or reconstitution step.

It depends on the application. For routine lab work, a 1% error in volume produces roughly a 1% error in concentration, which is usually acceptable. For analytical chemistry, quality control, or clinical assays, you may need 0.1% accuracy — which requires calibrated volumetric glassware or an analytical balance. General rules: use volumetric pipettes for volumes 1–25 mL, micropipettes for volumes below 1 mL, and graduated cylinders for volumes above 25 mL when moderate accuracy suffices. Always use class A volumetric glassware for standards. For very small volumes (below 10 µL), pipetting error can easily exceed 5%, so serial dilution is preferred over direct dilution.