Dilution calculator
Work out how much stock solution and diluent to mix for a working solution, or plan a serial dilution series.
C1 × V1 = C2 × V2
The dilution formula: C1V1 = C2V2
Diluting a solution adds solvent but no solute, so the amount of solute is the same before and after: C1 × V1 = C2 × V2. C1 and V1 are the stock's concentration and the volume of it you take; C2 and V2 are the concentration and volume you end up with. To make 10 mL of 1× buffer from a 10× stock, take 10 × 1 ÷ 10 = 1 mL of stock and add 9 mL of diluent. Enter any three values and the calculator finds the fourth.
Both concentrations must be the same kind of unit, both molar or both mass, because the formula only scales them. To mix the two, convert one first with the molarity calculator.
How to calculate a dilution factor
The dilution factor is how many times weaker the final solution is: dilution factor = C1 ÷ C2 = V2 ÷ V1. Taking 1 mL of stock up to 10 mL is a dilution factor of 10, written 1 in 10 or 1:10. Dilution factors multiply, so two 1 in 10 steps make a 1 in 100 dilution.
The serial dilution formula
In a serial dilution each tube is diluted from the one before by the same factor, so tube n holds starting concentration ÷ factorⁿ. For a factor of 10 and 1 mL per tube, each tube starts with 0.9 mL of diluent and receives 0.1 mL from the tube before. Mix each tube well before the next transfer and use a fresh tip each time, since carry-over compounds down the series.
Small transfer volumes are the least accurate step, so check them against your pipette's range. The guide to molarity, mg/mL and dilutions covers the formulas in more depth.