Dilution calculator: C₁V₁ = C₂V₂, serial dilutions and dilution factors
Work out stock and diluent volumes in molar units, mass units or plain fold dilutions — and plan a whole serial series in one go.
Stock → working solution C₁V₁ = C₂V₂
Leave exactly one box blank and it will be filled in.
Dilution factor and parts
Translate between “1:20”, “20-fold”, “5 % of final volume” and actual pipetting volumes.
Serial dilution planner
Constant fold-change per step, constant transfer volume — the layout most plate assays use.
| Step | Concentration | Transfer in | Diluent | Cumulative dilution |
|---|
Mixing two solutions
Combine a concentrated and a dilute (or blank) solution and get the result — or work backwards to hit a target.
Reading dilution notation
Three notations are used interchangeably and they do not all mean the same thing:
| Written as | Usual meaning in life science | Example on 1 mL final |
|---|---|---|
| 1:10, 1 in 10, 10-fold | Final volume is 10× the stock volume | 100 µL stock + 900 µL diluent |
| 1 + 9 | 1 part stock plus 9 parts diluent (unambiguous) | 100 µL stock + 900 µL diluent |
| 10 % (v/v) | Stock is 10 % of the final volume | 100 µL stock + 900 µL diluent |
| 1:10 (chemistry convention) | 1 part stock to 10 parts diluent — an 11-fold dilution | 91 µL stock + 909 µL diluent |
When you write a protocol, give the final volume and the stock volume explicitly. “Add 100 µL of stock to 900 µL of buffer” can only be read one way.
Practical points
- Never pipette below about 2 µL with an air-displacement pipette if accuracy matters. If a calculation asks for 0.4 µL, make an intermediate dilution instead.
- Dilution errors compound in a serial series. A 2 % error per step becomes an 18 % error by the ninth point. Mix thoroughly and change tips between steps.
- Volumes are not always additive. For concentrated ethanol, glycerol or sulfuric acid, dissolve and then make up to the final volume in a graduated vessel rather than adding a calculated volume of water.
- Viscous stocks carry over. Glycerol, Ficoll and detergent stocks leave film on the tip; reverse-pipette or pre-wet the tip.
Frequently asked questions
What does C1V1 = C2V2 mean?
It states that the amount of solute is conserved during dilution. C₁ and V₁ are the concentration and volume of the stock you take; C₂ and V₂ are the concentration and volume of the final solution. Rearranged, V₁ = C₂V₂ / C₁.
How do I make a 1:10 dilution?
Take 1 part stock and add 9 parts diluent to reach 10 parts total. A "1:10 dilution" means a 10-fold dilution — 1 mL of stock plus 9 mL of buffer, not 10 mL of buffer.
Is a 1:5 dilution the same as a 1 in 5 dilution?
In most life-science protocols yes: both mean the final volume is 5× the stock volume (1 part stock + 4 parts diluent). Some chemistry texts read "1:5" as 1 part in 5 parts of diluent (6 parts total), so state the final volume explicitly to avoid ambiguity.
How do I plan a serial dilution?
Choose a constant dilution factor per step (commonly 2-, 5- or 10-fold), carry a fixed transfer volume into a fixed diluent volume, and mix thoroughly between steps. The concentration after n steps is C₀ / factorⁿ.