Dilution Calculator
Calculate dilutions using C1V1 = C2V2
C1V1 = C2V2
Enter any 3 values to calculate the 4th
About the Dilution Formula
The dilution equation C1V1 = C2V2 relates the concentration and volume of a solution before and after dilution. C1 and V1 are the initial concentration and volume, while C2 and V2 are the final values.
This calculator is commonly used in laboratory settings for preparing standard solutions, serial dilutions, and adjusting reagent concentrations.
Understanding Dilution
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent. The total amount of solute remains the same before and after dilution — only the concentration changes. This relationship is expressed mathematically as C1V1 = C2V2, where the product of concentration and volume is constant.
Concentration can be expressed in various units including molarity (M), percent concentration, parts per million (ppm), or any consistent unit. Volume is typically measured in liters (L) or milliliters (mL). As long as both sides use the same units, the equation works correctly.
Common Applications
- Laboratory preparation: Preparing working solutions from concentrated stock solutions.
- Serial dilutions: Creating a series of progressively more dilute solutions for calibration curves or biological assays.
- Pharmaceutical compounding: Adjusting drug concentrations for specific dosage requirements.
- Environmental testing: Diluting water samples to measurable concentration ranges for analysis.
How to Use This Calculator
Enter any three of the four values — initial concentration (C1), initial volume (V1), final concentration (C2), and final volume (V2) — and the calculator will solve for the missing value. Leave the unknown field blank or set it to zero, then click calculate.
Worked example: preparing a working solution from stock
You have a 2.0 M stock solution and need 500 mL of 0.10 M working solution. This is the everyday application of C1V1 equals C2V2.
- Identify what you know. C1 is the stock concentration of 2.0 M, C2 is the target concentration of 0.10 M, and V2 is the target volume of 500 mL. V1, the volume of stock required, is the unknown.
- Rearrange the equation. V1 equals C2 times V2 divided by C1.
- Substitute. V1 equals 0.10 times 500 divided by 2.0, which is 25 mL.
- Carry it out correctly. Measure 25 mL of stock into a 500 mL volumetric flask, then add solvent up to the 500 mL graduation mark.
Answer. Take 25 mL of the 2.0 M stock and dilute to a final volume of 500 mL. Note the wording: you dilute to 500 mL, you do not add 500 mL.
Common mistakes
These are the errors that come up most often, and each one changes the answer rather than merely looking untidy.
Adding the solvent volume instead of diluting to volume
Adding 475 mL of water to 25 mL of stock is not the same as making the total up to 500 mL, because volumes are not perfectly additive when solutions mix. For dilute aqueous work the difference is small, but for concentrated solutions such as sulfuric acid it is significant, and the habit of diluting to a graduation mark is what analytical accuracy depends on.
Mixing units between the two sides
The equation works with any volume unit provided both sides use the same one. Putting millilitres on one side and litres on the other produces an answer wrong by a factor of a thousand, which at least tends to be obvious.
Applying the formula across a chemical change
C1V1 equals C2V2 assumes the amount of solute is unchanged and only the volume differs. It does not apply if the solute reacts, precipitates, or if you are mixing two different solutes.
Adding water to concentrated acid
This is a safety point rather than an arithmetic one. Always add concentrated acid to water, never the reverse. The heat of dilution can boil the water at the point of contact and spatter acid. The calculation is the same either way; the procedure is not.
Frequently asked questions
Does the dilution equation work for percentage concentrations?
Yes. The relationship holds for any concentration unit as long as both concentrations are expressed in the same one, whether that is molarity, percent by mass, or parts per million.
What is a serial dilution?
A sequence of dilutions where each step uses the product of the previous one as its stock. It is the practical way to reach very low concentrations, because a single step from a concentrated stock to a very dilute target would require measuring an impractically small volume.
Does temperature affect a dilution calculation?
Only slightly, and indirectly. Molarity is defined per litre of solution, and liquid volumes expand as temperature rises, so a solution prepared at one temperature is fractionally less concentrated when warmed. For precise work, prepare and use solutions at the same temperature.
What is the dilution factor?
The ratio of final volume to initial volume, which for this example is 500 divided by 25, or 20. The concentration falls by the same factor, so a 20 fold dilution takes 2.0 M down to 0.10 M.