Serial Dilution Calculator

Six tenfold steps reach one part in a million using comfortable volumes at every stage.

After 6 serial steps at this factor1 × 10⁻⁶each step repeats the same dilution on the previous tube

Stock to take100 mLmade up to 1,000 mL total

Solvent to add900 mL

Dilution factor1 : 10one part stock in 10 parts of finished solution

As a percentage of stock10%

Parts per million if the stock is a percentage1,000 ppmread this row only when the concentrations above are percentages

Serial dilution reaches concentrations that a single step cannot measure out: a millionfold dilution in one go would need a microlitre of stock in a litre of solvent, but six tenfold steps each move a comfortable volume.

The formula

C1 * V1 = C2 * V2 ; dilution factor = C1 / C2

Why the solute is conserved

Adding solvent changes the volume and nothing else, so the number of moles on each side of the equation is identical. That single fact is the whole of C₁V₁ = C₂V₂, and it is why the relation holds whatever units the concentration is quoted in — molar, percent or parts per million — provided both sides use the same one.

Serial rather than single

A single millionfold dilution would need one microlitre of stock measured into a litre of solvent, and the pipetting error would swamp the result. Six tenfold steps move a comfortable volume every time and arrive at the same place, which is why plate counts and standard curves are always built this way.

Which denominator?

Most of the confusion in solution work is not arithmetic but bookkeeping. Molarity divides by the volume of the finished solution; molality divides by the mass of the solvent; percent by mass divides by the mass of the solution again. The three agree closely in dilute water and diverge sharply in concentrated acid, which is why a bottle labelled 98 % is also labelled 18.4 M without contradiction.