Dilutions

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.

C₁ × V₁ = C₂ × V₂  →  V₁ = C₂V₂ / C₁
Concentration units

Dilution factor and parts

Translate between “1:20”, “20-fold”, “5 % of final volume” and actual pipetting volumes.

dilution factor = Vfinal / Vstock  ·  Vdiluent = Vfinal − Vstock
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Serial dilution planner

Constant fold-change per step, constant transfer volume — the layout most plate assays use.

Cn = C₀ / factorn  ·  transfer = Vstep / factor
StepConcentrationTransfer inDiluentCumulative dilution

Mixing two solutions

Combine a concentrated and a dilute (or blank) solution and get the result — or work backwards to hit a target.

Cmix = (C₁V₁ + C₂V₂) / (V₁ + V₂)

Reading dilution notation

Three notations are used interchangeably and they do not all mean the same thing:

Written asUsual meaning in life scienceExample on 1 mL final
1:10, 1 in 10, 10-foldFinal volume is 10× the stock volume100 µL stock + 900 µL diluent
1 + 91 part stock plus 9 parts diluent (unambiguous)100 µL stock + 900 µL diluent
10 % (v/v)Stock is 10 % of the final volume100 µL stock + 900 µL diluent
1:10 (chemistry convention)1 part stock to 10 parts diluent — an 11-fold dilution91 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.

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