Dilution Calculator
Enter your stock concentration, the concentration you want, and the final volume to find how much stock solution and solvent to combine.
The dilution equation C₁V₁ = C₂V₂ relates the concentration and volume before and after dilution. To make a diluted solution, the volume of stock you need is V₁ = C₂V₂ ÷ C₁, and the solvent you add is V₂ − V₁. To make 500 mL of 0.1 M solution from a 1 M stock, take 50 mL of stock and add 450 mL of solvent.
How to Use This Calculator
Enter three values: your stock (starting) concentration C₁, the target concentration C₂ you want after diluting, and the final total volume V₂ you want to make. Concentration can be in any unit — molarity, mg/mL, percent — as long as C₁ and C₂ use the same unit. The calculator returns how much stock solution to measure out and how much solvent (usually water) to add.
This is the everyday tool for preparing working solutions from a concentrated stock, whether you are a student in a teaching lab, a researcher making buffers, or mixing a concentrate at home. The one rule: C₁ and C₂ must share the same concentration unit, and V₁ comes out in the same volume unit as V₂.
How the Calculation Works
Diluting a solution adds solvent but does not add or remove solute, so the number of moles (or grams) of solute stays constant. Concentration × volume equals the amount of solute, which gives the dilution equation C₁V₁ = C₂V₂. Rearranging for the unknown stock volume: V₁ = C₂V₂ ÷ C₁. The solvent you then add is simply the final volume minus the stock volume, V₂ − V₁. Because concentration goes down exactly as volume goes up, a 10-fold dilution means one part stock to nine parts solvent.
Worked Example
You have a 1 M stock solution and need 500 mL of 0.1 M working solution. V₁ = C₂V₂ ÷ C₁ = (0.1 × 500) ÷ 1 = 50 mL of stock. Solvent to add = 500 − 50 = 450 mL. So you measure 50 mL of the 1 M stock into a container and add 450 mL of solvent, giving 500 mL of 0.1 M solution — a 10× dilution, consistent with the concentration dropping from 1 M to 0.1 M.
What the Result Means
The first number is the volume of concentrated stock to measure; the second is the volume of solvent to add to reach your final volume. Add the stock to the solvent (or bring to volume in a volumetric flask) and mix. If the target concentration is much smaller than the stock, you will use very little stock — for extreme dilutions, a serial dilution (diluting in several steps) is more accurate than trying to measure a tiny single volume. The equation works identically for any concentration unit, which is why it is one of the most-used formulas in the lab.
Assumptions and Limitations
The equation assumes volumes are additive and that the solute amount is conserved — true for ordinary dilutions with water or a compatible solvent. It ignores small volume changes on mixing, which are negligible for dilute aqueous solutions but can matter for concentrated acids or alcohols; for those, bring to final volume in a volumetric flask rather than simply adding the calculated solvent. The target concentration must be lower than the stock — you cannot concentrate a solution by adding solvent.
Who Uses a Dilution Calculator
Chemistry students and lab technicians use this to find how much stock solution to use with the C1V1 = C2V2 equation. Run it at the bench when diluting a concentrated stock to a working concentration, so you measure the right volumes. Enter the concentrations and final volume to get the stock and solvent amounts.
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Open calculator →Frequently Asked Questions
What is the C1V1 = C2V2 formula used for?
It calculates how to dilute a concentrated stock solution to a lower concentration. C₁ and V₁ are the stock's concentration and volume; C₂ and V₂ are the diluted solution's concentration and volume.
How do I make a 1:10 dilution?
Use one part stock to nine parts solvent, giving a total of ten parts. For 500 mL total, that is 50 mL stock plus 450 mL solvent, which lowers the concentration to one-tenth of the stock.
Do C1 and C2 need the same units?
Yes. As long as both concentrations use the same unit (molarity, mg/mL, percent, etc.), the equation works and V₁ comes out in the same volume unit as V₂.
What if I need a very large dilution?
For dilutions beyond about 100-fold, use a serial dilution — several smaller dilution steps in sequence — because measuring one tiny volume of stock accurately is difficult and error-prone.
Can I use this for percent solutions?
Yes. The dilution equation is unit-agnostic. Enter both concentrations as percentages and the volumes will still balance correctly.
Should I add stock to solvent or solvent to stock?
For most solutions it does not matter, but when diluting concentrated acids always add acid to water, never water to acid, to safely dissipate the heat released.
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