Dilution calculator (C₁V₁ = C₂V₂)
To dilute a stock, use C₁V₁ = C₂V₂: the volume of stock needed is V₁ = C₂ × V₂ / C₁, topped up with diluent to V₂. Enter any three values to get the fourth, with molar, mass, percent or ×-fold units, or plan a serial dilution with the transfer and diluent volume for every tube.
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What it does
How to use the dilution calculator
- Choose single or serialUse C₁V₁ = C₂V₂ for one dilution, or the serial dilution planner for a series.
- Enter the known valuesPick what to solve for and fill in the other three values with their units.
- PipetteFollow the instruction: how much stock, how much diluent, or the volumes for each tube of the series.
How it works
C₁ × V₁ = C₂ × V₂
The amount of solute is the same before and after dilution. Concentrations must be in the same kind of unit (molar with molar, mass/volume with mass/volume). For a serial dilution with factor f and final volume V per tube, each tube holds V of diluent and receives V/(f − 1) from the previous tube; tube k has concentration C₀ / fk.
Worked example
To make 1 mL of 1 mM from a 10 mM stock: V₁ = 1 mM × 1 mL / 10 mM = 100 µL of stock plus 900 µL of diluent (a 1:10 dilution).
Frequently asked questions
What does C1V1 = C2V2 mean?
C₁ and V₁ are the concentration and volume of the stock you take; C₂ and V₂ are the concentration and total volume after dilution. The equation holds because dilution does not change the amount of solute.
Is a 1:10 dilution 1 part in 10 or 1 part plus 10?
In most lab usage 1:10 means 1 part sample in 10 parts total (1 + 9 diluent). Some fields use 1:10 for 1 part plus 10; check your protocol.
Can I convert between mM and mg/mL?
Only with the molar mass. Use the molarity calculator to convert, then dilute in one kind of unit.
How do I make a 2-fold serial dilution?
Choose serial dilution, factor 2: each tube gets the final volume of diluent and the same volume transferred from the previous tube, mixing at every step.
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