Dilution calculator
Solve the dilution equation C1V1 = C2V2 for any one value: how much stock to take, how far to dilute, or what concentration you end up with. Mix units freely, and plan a serial dilution below.
The greyed field is the one being calculated. Units can differ between fields, the calculator converts them.
Volume of stock to take
25mL
How to make it
Take 25 mL of the stock and add 225 mL of solvent to reach 250 mL in total.
C1 × V1 = C2 × V2 → 1 M × 25 mL = 0.1 M × 250 mL
How the calculation works
Diluting a solution adds solvent but no solute, so the amount of solute is the same before and after. Amount equals concentration times volume, which gives the dilution equation.
- C1
- concentration of the stock solution
- V1
- volume of stock you take
- C2
- concentration of the diluted solution
- V2
- final total volume after dilution
Rearrange for the value you need, for example V1 = C2 × V2 ÷ C1. The volume of solvent to add is V2 − V1, and the dilution factor is C1 ÷ C2 = V2 ÷ V1. Any concentration unit works as long as C1 and C2 use the same kind of unit, and any volume unit works as long as you convert V1 and V2 consistently. The calculator does the conversions for you.
The equation is for diluting with pure solvent. To blend two solutions of different strength use C1V1 + C2V2 = Cf × (V1 + V2), and remember that some liquids, such as ethanol and water, shrink slightly when mixed, so fill to the mark rather than adding volumes.
Worked example
The same steps the calculator follows, done by hand
You need 250 mL of 0.1 M hydrochloric acid and you have a 1 M stock.
- 1Write down what you know: C1 = 1 M, C2 = 0.1 M, V2 = 250 mL. V1 is unknown.
- 2Rearrange: V1 = C2 × V2 ÷ C1 = 0.1 × 250 ÷ 1 = 25 mL.
- 3Solvent to add: 250 − 25 = 225 mL. The dilution factor is 1 ÷ 0.1 = 10, a 1 in 10 dilution.
- 4Starting from concentrated acid at about 12.1 M instead, V1 = 0.1 × 250 ÷ 12.1 = 2.07 mL. Always add acid to water, never water to acid, and work in a fume hood with eye protection.
Serial dilution planner
Repeat the same dilution step to cover a wide range, such as a calibration curve
For each step move 100 µL from the previous tube into 900 µL of solvent and mix well.
| Tube | Concentration | Total dilution | Made from |
|---|---|---|---|
| Stock | 1 mM | 1 | Starting solution |
| 1 | 0.1 mM | 1 in 10 | 100 µL of stock + 900 µL solvent |
| 2 | 0.01 mM | 1 in 100 | 100 µL of tube 1 + 900 µL solvent |
| 3 | 0.001 mM | 1 in 1,000 | 100 µL of tube 2 + 900 µL solvent |
| 4 | 0.0001 mM | 1 in 10,000 | 100 µL of tube 3 + 900 µL solvent |
| 5 | 1 × 10⁻⁵ mM | 1 in 100,000 | 100 µL of tube 4 + 900 µL solvent |
| 6 | 1 × 10⁻⁶ mM | 1 in 1,000,000 | 100 µL of tube 5 + 900 µL solvent |