Dilution Calculator
Solve C₁V₁ = C₂V₂ for any missing variable. Choose your concentration and volume units.
Formula: C₁V₁ = C₂V₂
V₂ = 1000.0000 mL
What is a dilution calculator?
A dilution calculator determines the volumes and concentrations needed when mixing solutions. The fundamental principle is conservation of solute: the amount of dissolved substance stays the same before and after dilution. This is expressed by the formula C1*V1 = C2*V2, where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final values.
Dilution calculations are essential in chemistry labs, pharmacies, clinical settings, and industrial processes. Whether you are preparing a laboratory reagent, mixing cleaning solutions, or diluting a stock solution for an experiment, getting the concentration right is critical for accurate results and safety.
The dilution equation
C1 * V1 = C2 * V2. To find how much stock solution to use: V1 = (C2 * V2) / C1. For example, to make 500 mL of 0.1 M HCl from a 1.0 M stock solution: V1 = (0.1 * 500) / 1.0 = 50 mL of stock solution, diluted to 500 mL with water.
How to use this tool
Enter three of the four values (C1, V1, C2, V2) and the calculator solves for the missing one. The tool supports various concentration units (molarity, percentage, mg/mL) and volume units (mL, L). It also shows the volume of solvent (water or diluent) to add.
Serial dilutions
A serial dilution is a series of stepwise dilutions where each step dilutes the previous solution by a fixed ratio. A 1:10 serial dilution over 5 steps creates concentrations of 1/10, 1/100, 1/1000, 1/10000, and 1/100000 of the original. Serial dilutions are commonly used in microbiology (bacterial colony counting), immunology (antibody titers), and pharmacology (dose-response curves).
Safety considerations
When diluting strong acids, always add acid to water — never water to acid. Adding water to concentrated acid can cause a violent exothermic reaction, splashing hot acid. This rule is summarized as "do as you oughta, add acid to water." Wear appropriate personal protective equipment and work in a well-ventilated area.
Frequently asked questions
Does C1V1 = C2V2 work for all solutions?
The equation works when the solute does not change during dilution — no chemical reactions, precipitation, or volume changes from mixing. It is accurate for most aqueous dilutions at moderate concentrations. For very concentrated solutions or solutions where mixing causes significant volume changes (like ethanol-water mixtures), the approximation becomes less accurate.
What is the difference between dilution and concentration?
Dilution decreases the concentration of a solution by adding more solvent. Concentration (or evaporation) increases it by removing solvent. Both processes conserve the amount of solute. The C1V1 = C2V2 equation applies to dilution only — for concentration by evaporation, you need to account for the volume of solvent removed.