Dilution calculator
Solve C₁V₁ = C₂V₂ for any variable and see the dilution factor and the diluent to add — or plan a serial dilution with per-tube transfer and diluent volumes.
The formula
C₁V₁ = C₂V₂
- C₁
- concentration of the stock solution
- V₁
- volume of stock to transfer
- C₂
- concentration of the diluted solution
- V₂
- final volume of the diluted solution
Worked example
Prepare 250 mL of 0.5 M HCl from a 10 M stock — then a 10× series
Solve for V₁: V₁ = C₂V₂ / C₁ = (0.5 mol/L × 250 mL) / 10 mol/L = 12.5 mL of stock. Pipette it into a 250 mL volumetric flask already holding most of the diluent (acid into water, never water into concentrated acid) and make up to the mark — a 20× dilution. The 237.5 mL of diluent the calculator reports is the nominal figure V₂ − V₁; fill to the mark rather than measuring it out, because mixing volumes are not strictly additive.
Serial dilution: to step a 100 ppm standard down 10× per tube across five 10 mL tubes: transfer 1 mL, add 9 mL of diluent, mix, and repeat from the new tube. Concentrations run 10, 1, 0.1, 0.01, 0.001 ppm.
Common pitfalls
Adding V₂ of diluent instead of diluting to volume
V₂ is the final solution volume, not the diluent volume. Transfer the stock, then make up to the mark in a volumetric flask. Adding 250 mL of water to 12.5 mL of stock gives 262.5 mL of something else.
Expecting a dilution to raise concentration
If the numbers ask for C₂ above C₁, it is not a dilution and this calculator refuses to solve it. Start from a stronger stock, or concentrate by another route.
The sampled tube of a serial dilution ends short
Every tube except the last gives up one transfer volume to the next tube. If each step must retain its full stated volume — an instrument read, for example — plan a larger tube volume to cover the loss.
Mixing unit families
Converting mg/L to mM needs the analyte's molecular weight — that is a molarity question, not a dilution question. Keep C₁ and C₂ in the same unit family here, or translate first with the molarity calculator.