Dilution Calculator (C1V1 = C2V2)

This dilution calculator uses the relationship C1V1 = C2V2 and solves for whichever of the four variables you do not know: the stock concentration (C1), the volume of stock to use (V1), the desired final concentration (C2), or the total final volume (V2). Diluting a concentrated stock solution is one of the most common tasks in chemistry, biology, microbiology, and everyday settings such as brewing, pool maintenance, cleaning products, and hydroponics. The principle is straightforward: when you dilute a solution by adding solvent (usually water), the amount of solute does not change, so the product of concentration and volume stays constant before and after. You choose which variable to solve for, enter the three known values, and the calculator returns the answer along with the volume of diluent to add and the dilution factor. The only rule is that units must be consistent: use the same concentration unit (mol/L, percent, g/L) for both concentrations, and the same volume unit (mL or L) throughout. The calculated diluent volume is the final volume minus the stock volume, and the dilution factor is how many times more dilute the final solution is compared to the stock. Note that you cannot dilute to a concentration higher than the stock, so C2 must always be less than C1. The default example dilutes a 10 mol/L stock to 2 mol/L by taking 25 mL of stock and making it up to a final volume of 125 mL with diluent. Results are theoretical and assume ideal mixing with no volume change on mixing.

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25
stock volume to use (V1)
Stock volume (V1)25
Diluent to add100
Final volume (V2)125
Dilution factor5x

Use the same concentration unit for C1 and C2 (mol/L, %, g/L) and the same volume unit for V1 and V2 (mL or L). The final concentration must be lower than the stock concentration.

How it works

Rearranging C1V1 = C2V2: to find V1 use C2 x V2 / C1; to find V2 use C1 x V1 / C2; to find C1 use C2 x V2 / V1; to find C2 use C1 x V1 / V2. The diluent volume to add is always V2 minus V1. The dilution factor is C1 / C2, which tells you how many times more dilute the final solution is. Division by zero is caught and an error prompt is shown.

Worked example

You have a 10 mol/L stock solution and need 125 mL of a 2 mol/L solution. Using C1V1 = C2V2: V1 = (2 x 125) / 10 = 25 mL of stock. Add 100 mL of diluent to reach 125 mL total. The dilution factor is 10 / 2 = 5x. These are the default values pre-filled in the calculator above.

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Frequently asked questions

What is the dilution formula C1V1 = C2V2?

C1V1 = C2V2 states that the amount of solute before dilution equals the amount after. C1 is the initial (stock) concentration, V1 is the volume of stock used, C2 is the desired final concentration, and V2 is the total final volume. Rearranging: V1 = C2 x V2 / C1, which tells you how much stock to measure out.

How much diluent do I add?

The diluent (usually water) to add equals the final volume V2 minus the stock volume V1. For example, if V2 is 125 mL and V1 is 25 mL, you add 100 mL of water to 25 mL of stock to make up 125 mL total.

Do C1 and C2 have to be in mol/L?

No. Any consistent concentration unit works: mol/L, g/L, percent, or parts per million, as long as C1 and C2 use the same unit. Similarly, V1 and V2 can be in mL, L, or any other volume unit, as long as both use the same unit.