Dilution Calculator

How dilution works

Diluting a solution means adding more solvent to lower its concentration. The amount of solute stays the same; it is just spread through a larger volume. That simple idea gives the dilution equation, where the concentration times volume before equals the concentration times volume after.

C₁ and V₁ are the starting concentration and volume, and C₂ and V₂ are the final ones. Knowing any three lets you solve for the fourth, which is exactly what this calculator does.

How to use this calculator

1. Enter the starting concentration \(C_1\) and the starting volume \(V_1\).
2. Enter the desired final concentration \(C_2\) and final volume \(V_2\), or use the calculator to find the missing value.
3. Check that all concentration units match, such as \(\%\), \(\text{mol/L}\), or \(\text{mg/mL}\).
4. Read the result, which tells you the amount of stock solution or the final diluted amount, depending on the value you solved for.

The formula explained

The dilution formula \(C_1V_1 = C_2V_2\) says that the amount of solute stays the same before and after dilution. It computes the relationship between the starting solution and the diluted solution.

• \(C_1\) = starting concentration of the stock solution
• \(V_1\) = starting volume of the stock solution
• \(C_2\) = final concentration after dilution
• \(V_2\) = final total volume after dilution

Step by step method

1. Write the dilution equation \(C_1V_1 = C_2V_2\).
2. Rearrange it to solve for the unknown value, for example \(V_1 = \frac{C_2V_2}{C_1}\) if you need the starting volume.
3. Substitute the numbers, then divide or multiply to get the answer.

Worked example

Problem. You want to make \(250\\,\text{mL}\) of a \(0.40\\,\text{M}\) solution from a \(2.0\\,\text{M}\) stock solution. How much stock solution do you need?

1. Use \(C_1V_1 = C_2V_2\).
2. Solve for \(V_1\): \(V_1 = \frac{C_2V_2}{C_1} = \frac{(0.40)(250)}{2.0}\).
3. Compute \(V_1 = 50\\,\text{mL}\).

Tips and common mistakes

• Make sure the concentration units on both sides are the same before you calculate.
• If you are adding water or another solvent, the final volume is the total volume after mixing, not just the solvent you add.

Frequently asked questions