Labs keep concentrated stock solutions and dilute them as needed. Enter the stock concentration, the target concentration and the final volume to see how much stock to measure and how much water to add.
Enter the stock and target concentrations in the same unit.
Enter the final volume you need.
Measure V₁ of stock and top up with diluent.
Dilution: C₁ V₁ = C₂ V₂
Stock volume: V₁ = C₂ V₂ ÷ C₁
Labs rarely make every solution from scratch. They keep a concentrated stock and dilute it when needed. This calculator uses C₁V₁ = C₂V₂ to tell you how much stock solution to measure out, and how much water or other diluent to add, to reach a target concentration and final volume.
It works with any concentration unit, as long as the stock and target use the same one: molarity, percent, mg/mL or ppm. That makes it useful beyond chemistry class, for diluting disinfectant, preparing fertiliser sprays for a farm, or making up cleaning solutions in a hospital or kitchen. It also warns you if the target is stronger than the stock, because adding solvent can never make a solution more concentrated.
1. Write the stock concentration C₁ and the target concentration C₂ in the same unit.
2. Decide the final volume V₂ you need.
3. Calculate the stock volume: V₁ = C₂ × V₂ ÷ C₁. It comes out in the same unit as V₂.
4. Calculate the diluent needed: V₂ − V₁.
5. Measure V₁ of stock into a volumetric flask or cylinder, then add diluent up to the final volume V₂.
6. For strong acids, place most of the water in the vessel first and add the acid to it slowly.
Concentration is the amount of solute per unit volume. Multiply it by volume and you get the amount of solute itself, in moles, grams or whatever the unit implies. Dilution adds only solvent, so the amount of solute before and after is the same. Setting the two amounts equal gives C₁V₁ = C₂V₂. The law is a statement of conservation of solute, not a special chemical rule, which is why it works for sugar syrup as well as hydrochloric acid.
The diluent figure V₂ − V₁ assumes that volumes add. For dilute aqueous solutions this is close enough. For concentrated acids, alcohol and water, or other strongly interacting liquids, the mixture's volume can be slightly less than the sum, and heat is released. That is why careful work adds the stock to a volumetric flask and then fills to the mark, rather than measuring the diluent separately. The final volume, not the volume of water added, is what C₂ refers to.
To get very low concentrations, a single dilution would need a tiny, hard-to-measure V₁. Instead labs dilute in stages, for example 1 in 10 repeated three times to make a 1 in 1000 dilution. Each stage uses C₁V₁ = C₂V₂ with the previous stage's solution as the new stock. The overall dilution factor is the product of the stage factors. Microbiology labs use this to count bacteria, and analytical labs use it to prepare calibration standards.
A lab technician at a college in Chandigarh has 6 M hydrochloric acid stock and needs 500 mL of 0.25 M acid for a class practical.
C₁ V₁ = C₂ V₂ → V₁ = C₂ V₂ ÷ C₁: V₁ = 0.25 × 500 ÷ 6 = 20.8333 mL
Diluent to add: 500 − 20.8333 = 479.1667 mL
Answer: Stock solution needed (V₁) 20.8333 mL; Water / diluent to add 479.1667 mL
Mixing units, such as a stock in % and a target in M, without converting.
Adding V₂ of water to V₁ of stock, which makes the total too large and the solution too weak.
Swapping C₁ and C₂, which gives a stock volume larger than the final volume.
Adding water to concentrated acid, which can boil and splash; always add acid to water.
Trying to reach a target stronger than the stock by dilution.
Preparing working solutions from stock reagents in school and college labs.
Diluting disinfectants and sanitisers to the strength printed on the label.
Mixing pesticide or fertiliser sprays for fields and gardens.
Preparing calibration standards and serial dilutions in analytical and microbiology labs.
Making up buffer and media solutions in biotechnology work.
Can I use percentages?
Yes, as long as both concentrations are percentages.
Should I add acid to water or water to acid?
Always add acid to water, slowly, for safety.