About the Dilution Calculator
This dilution calculator solves the equation C₁V₁ = C₂V₂ for whichever value you are missing. Typically you know the concentration of your stock solution, the concentration you want and the final volume you need — the calculator tells you how much stock to pipette and how much water or buffer to add to reach that volume.
It is built for lab work in chemistry, biology and medicine: making working solutions from a 10X buffer, diluting a 1 M stock to millimolar, preparing percentage solutions or diluting antibodies in µg/mL. A serial dilution table shows the concentrations you get from repeating the same dilution step several times.
The concentration and volume units just need to be consistent on both sides of the equation — the calculator uses the unit you choose for both C₁ and C₂ and for both V₁ and V₂. It assumes volumes are additive, which is accurate for dilute aqueous solutions.
How to use the dilution calculator
- 1Choose the value you want to find — usually the stock volume V₁.
- 2Select the concentration unit and volume unit you are working in.
- 3Enter the three known values.
- 4Pipette V₁ of stock and top up with solvent to the final volume V₂.
- 5Use the serial dilution table if you need a series of weaker solutions.
Formula and method
When you dilute a solution the amount of solute does not change — you only add solvent. The amount of solute is concentration × volume, so the stock concentration times the stock volume must equal the final concentration times the final volume. Rearranging gives V₁ = C₂V₂ ÷ C₁, C₂ = C₁V₁ ÷ V₂, and so on.
The volume of solvent to add is V₂ − V₁, and the dilution factor is C₁ ÷ C₂ (equivalently V₂ ÷ V₁). In a serial dilution the same factor is applied repeatedly, so after n steps the concentration is C₁ ÷ factorⁿ.
- C₁
- Concentration of the stock solution
- V₁
- Volume of stock solution used
- C₂
- Concentration of the diluted solution
- V₂
- Total volume of the diluted solution
Worked examples
Make 250 mL of 0.5 M from a 2 M stock
V₁ = 0.5 M × 250 mL ÷ 2 M = 62.5 mL of stock. Add 187.5 mL of water to reach 250 mL. This is a 1:4 dilution.
Dilute a 10X buffer to 1X
To make 500 mL of 1X buffer from 10X stock, use 1 × 500 ÷ 10 = 50 mL of stock and 450 mL of water.
Final concentration after diluting 5 mL of 70%
Diluting 5 mL of a 70% solution to a total of 35 mL gives C₂ = 70 × 5 ÷ 35 = 10%. You add 30 mL of diluent for a 7-fold dilution.
Frequently asked questions
What does C1V1 = C2V2 mean?+
It states that the amount of solute before dilution (stock concentration × stock volume) equals the amount after dilution (final concentration × final volume), because diluting only adds solvent.
Is V2 the volume of water to add?+
No. V₂ is the total final volume. The amount of water or buffer to add is V₂ − V₁. For example, 62.5 mL of stock made up to 250 mL needs 187.5 mL of water.
Can I use percent or mg/mL with this formula?+
Yes. Any concentration unit works as long as C₁ and C₂ use the same unit and V₁ and V₂ use the same unit. Molarity, percent, mg/mL and X strength all work.
What is a dilution factor?+
The dilution factor is the ratio of stock to final concentration (C₁ ÷ C₂), or final to stock volume. A 1:10 dilution has a factor of 10, meaning the solution is ten times weaker.
How does a serial dilution work?+
You repeat the same dilution step several times, each time using the previous tube as the stock. Three successive 1:10 dilutions give a total dilution of 1:1,000.