Molarity & Dilution Calculator (C1V1=C2V2)
Use the dilution formula C1V1 = C2V2 to calculate any one of the four values (concentration or volume, before and after dilution) from the other three.
What Are Molarity and Dilution Calculations?
Molarity and dilution calculations let you figure out the relationship between concentration and volume whenever you're diluting a solution down to a different, lower concentration. In the lab (and even in the kitchen), you'll often need to answer questions like "how much should I dilute my stock solution to reach the concentration I want?" or "how many mL of stock do I need to make a target volume at a target concentration?" This tool handles all of that using the dilution formula C1V1 = C2V2 (concentration before dilution × volume before dilution = concentration after dilution × volume after dilution), instantly solving for any one of the four values — two concentrations and two volumes — once you supply the other three.
The formula rests on one key assumption: the amount of solute, measured in moles, stays exactly the same before and after dilution. Adding solvent increases the total volume, but it doesn't add or remove any of the dissolved substance itself. Concentration values in this tool are standardized to mol/L and volumes to mL, so if your figures are in different units (liters, for instance), convert them first before typing them in. All of the math runs locally in your browser — nothing you enter is ever sent to a server.
How to Use the Molarity & Dilution Calculator
- Choose the value you want to solve for From "Value to solve for," pick which of the four variables you need: C1 (concentration before dilution), V1 (volume before dilution), C2 (concentration after dilution), or V2 (volume after dilution).
- Enter the other three values The three input fields for everything except your chosen variable will appear. Fill each one in with the values already fixed by your experiment or recipe.
- Read off the result The calculated result appears in the panel on the right as soon as you finish entering values. Concentration is shown in mol/L and volume in mL throughout.
Tips for getting more out of it
- Selecting the variable you want in "Value to solve for" reveals the remaining three input fields. Enter the three values already fixed by your experiment.
- Volume is standardized in mL and concentration in mol/L. If your numbers use different units (such as L), convert them before entering.
- When mixing solutions, it's safest to follow the "add acid to water" principle: add the concentrated stock solution gradually into a small amount of solvent, then top it up with more solvent.
- For accurate dilution, we recommend using precision glassware such as a volumetric pipette or a volumetric flask with fine graduations.
Where This Calculator Comes in Handy
Building a dilution series from a stock solution
When you need several different concentrations from one concentrated stock solution for an experiment, you can work out ahead of time exactly how much stock and how much solvent each dilution requires.
Preparing reagents and working out dilution ratios
Handy for converting an instruction like "dilute 1:10" into an actual concentration, or working backward from a target concentration to figure out the dilution ratio and stock volume you'll need. If you're starting from a substance amount instead, pair this with our molar mass calculator to get to a concentration first.
Adjusting the strength of disinfectants and cleaning solutions
Also useful for safely working out how much water and concentrate to combine when diluting a strong stock solution, such as sodium hypochlorite, down to a practical working concentration.
Pre-calculations for titration and analytical chemistry
Before running a titration, you can use this to determine the volume needed to dilute a standard solution to the target concentration. Once you've titrated, our pH calculator can help you work out the resulting pH.
Key Terms for Molarity & Dilution
- Molarity
- A unit of concentration expressing the amount of solute, in moles, dissolved per liter of solution — written as mol/L (or sometimes just M). It's calculated as "moles of solute ÷ liters of solution."
- Dilution
- The process of adding solvent (usually water) to a solution to increase its volume and lower its concentration. Because the actual amount of dissolved solute doesn't change, the concentration simply drops in proportion to the added volume.
- Solute
- The substance that's dissolved within a solution. In salt water, for example, the salt (sodium chloride) is the solute, and molarity is always calculated based on the solute's amount.
- Solvent
- The liquid that dissolves the solute. A solution where water is the solvent is called an aqueous solution, and water is by far the most common solvent used for dilutions in the lab.
- Stock solution
- A solution prepared at a high concentration before it's diluted down for use. Labs commonly keep concentrated stock solutions on hand for efficient storage and transport, diluting them to the needed concentration only when it's time to use them.
- Avogadro's number
- A constant linking the amount of a substance (in moles) to the number of particles it contains — about 6.022×10²³ particles per mole. The whole concept of molarity depends on this constant, since it's what lets us count matter on a particle basis in the first place.
Frequently Asked Questions
Side Note — Where the Unit "Molarity" Comes From
Molarity (mol/L, also written with the symbol M) only became possible as a concept thanks to the "Avogadro constant" (about 6.022×10²³) proposed by the Italian physicist Amedeo Avogadro in the late 19th century — a constant that bridges the gap between the amount of a substance and the number of particles it contains. Before that, solution concentration could only be expressed as a mass ratio, which made handling the quantitative relationships of chemical reactions (stoichiometry) extremely cumbersome.
The advent of molarity let chemists describe reactions using a unified scale of "how many moles of substance are dissolved" rather than "how many grams." Combined with the fact that the coefficients in a chemical equation directly represent molar ratios, this became the foundation of quantitative analytical chemistry — including titration — that is still widely used today.
The "volumetric flask" used for dilution in the laboratory is glassware designed to measure a specific volume accurately at a specific temperature (usually 20°C). Because both glass and liquids change volume slightly with temperature, controlling room temperature is also considered a factor affecting dilution accuracy in precise analytical chemistry work.