Lab / Solutions
Dilution Calculator (C₁V₁ = C₂V₂ and Serial Dilutions)
Work out how much stock solution to dilute, or the final concentration or volume, from C₁V₁ = C₂V₂ with units from molar to nanomolar and litres to microlitres, plus the diluent to add and a serial dilution table.
Dilution Calculator (C₁V₁ = C₂V₂ and Serial Dilutions): Diluting keeps the amount of solute the same, so C₁ × V₁ = C₂ × V₂. To make 50 mL of 10 mM from 100 mM stock, V₁ = 10 × 50 ÷ 100 = 5 mL: take 5 mL and add 45 mL of diluent. A serial dilution repeats one step: with a factor of 10, each tube is a tenth as strong as the last, and after 3 steps the total dilution is 1 : 1,000. Runs 100% locally in your browser with zero server file uploads.
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| Step | Concentration | Total dilution |
|---|---|---|
| 0 | 100 mM | 1 : 1 |
| 1 | 10 mM | 1 : 10 |
| 2 | 1 mM | 1 : 100 |
| 3 | 0.1 mM | 1 : 1,000 |
| 4 | 0.01 mM | 1 : 10,000 |
| 5 | 0.001 mM | 1 : 100,000 |
| 6 | 0.0001 mM | 1 : 1,000,000 |
The amount of solute stays the same when you dilute, so C₁ × V₁ = C₂ × V₂: to make 50 mL at 10 mM from a 100 mM stock, take 5 mL of stock and make it up to 50 mL. Use the same units on both sides. For a serial dilution, each step dilutes the previous one by the same factor, so after n steps the total dilution is the factor to the power n.
Worked examples
10 µL of a 1 mM stock in a final 1 mL gives 10 µM. To make 1 L of 70% ethanol from 95%: V₁ = 70 × 1000 ÷ 95 = 737 mL, made up to 1 L with water.
To work out the stock concentration from a weighed mass, use the molarity calculator.
Serial dilutions in practice
For bacterial counts, plate several steps of a 1 : 10 series so at least one plate has 30 to 300 colonies; multiply the count by the total dilution to get the original concentration.
For a standard curve, a 1 : 2 series halves the concentration at each step: 100, 50, 25, 12.5 µg/mL.
How to use it
- Choose the value to work out.
- Enter the other three, and pick the concentration and volume units.
- Read the answer, the diluent to add, and the serial dilution table.
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Frequently asked questions
Do the units have to match?
Concentrations must share one unit and volumes another; the tool keeps them consistent for you.
What does 1 : 10 mean?
One part stock in ten parts total: 1 mL of stock made up to 10 mL, which is 1 mL of stock plus 9 mL of diluent.
Can I dilute percentages or mg/mL?
Yes: C₁V₁ = C₂V₂ works for any concentration unit, as long as both concentrations use the same one.
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