The dilution formula (C1V1 = C2V2)
In chemistry and biology laboratories, solution dilution follows the conservation of solute mass: C1 × V1 = C2 × V2, where C1 is the initial stock concentration, V1 is the volume of stock solution, C2 is the desired final concentration, and V2 is the final total volume.
To find the volume of stock solution required to prepare a specific final volume at a target concentration, rearrange the equation to V1 = (C2 × V2) / C1. The amount of solvent (or diluent, such as deionised water or buffer) to add is the final volume minus the stock volume: V_diluent = V2 − V1.
The dilution factor represents the ratio of the stock concentration to the final concentration (C1 / C2), which is also equal to the final volume divided by the stock volume (V2 / V1). For example, diluting a 10 M solution to 1 M is a 10-fold (1:10) dilution.
Worked example
Suppose you have a 5 M NaCl stock solution and need to prepare 200 mL of 0.5 M NaCl solution for an experiment.
Using V1 = (C2 × V2) / C1: V1 = (0.5 M × 200 mL) / 5 M = 20 mL of stock solution.
The volume of diluent required is V2 − V1 = 200 mL − 20 mL = 180 mL of water or buffer. Adding 20 mL of 5 M stock to 180 mL of diluent gives exactly 200 mL of 0.5 M solution, with a dilution factor of 10.
Practical laboratory tips for accurate dilutions
Always add acid or concentrated stock to water rather than water to concentrated acid, especially when diluting strong acids like sulfuric or hydrochloric acid.
Ensure your volumetric glassware (such as volumetric flasks and pipettes) is clean and calibrated at room temperature (typically 20°C).
When mixing viscous solutions or solutions with significant heat of dissolution, allow the solution to equilibrate to room temperature before bringing it up to the final calibration mark on the volumetric flask.
Inputs for the dilution calculator
Calculation mode
Choose whether you are calculating how much stock volume you need to achieve a target concentration, or working out the resulting concentration from mixing known volumes.
Stock concentration (C1)
The strength of your initial starting solution. Make sure both concentrations use the same unit.
Final volume (V2)
The total volume of solution you wish to prepare after dilution, not the amount of diluent added.
CALCULATOR QUESTIONS
Solution dilution calculator questions
What is the formula for calculating dilution?
The formula is C1V1 = C2V2, where C1 is the initial concentration, V1 is the volume of stock solution, C2 is the final concentration, and V2 is the final total volume.
What does a 1:10 dilution mean?
A 1:10 dilution means 1 part of stock solution combined with 9 parts of diluent to make a total of 10 parts, resulting in a concentration that is one-tenth of the original stock.
Do units have to be molarity and millilitres?
No. As long as C1 and C2 share the same concentration unit (e.g. M, mM, mg/mL, or %) and V1 and V2 share the same volume unit (e.g. mL, L, or µL), the units cancel out correctly.
How do I perform a serial dilution?
A serial dilution is a stepwise series of dilutions using the same dilution factor at each step. For example, a 10-fold serial dilution takes 1 mL of each tube into 9 mL of diluent in the subsequent tube.