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Dilution Factor and Ratio Calculator

Find a dilution factor from volumes or concentrations, see it written both as sample : total and sample : diluent, or turn a factor into volumes to pipette.

Formula

DF=VfinalVsample\mathrm{DF} = \dfrac{V_{\text{final}}}{V_{\text{sample}}}
Vfinal=Vsample+VdiluentV_{\text{final}} = V_{\text{sample}} + V_{\text{diluent}}
DF=CstartCfinal\mathrm{DF} = \dfrac{C_{\text{start}}}{C_{\text{final}}}
Vsample=VfinalDFV_{\text{sample}} = \dfrac{V_{\text{final}}}{\mathrm{DF}}
DF\mathrm{DF}
dilution factor: how many times less concentrated the sample has become
sample : total\text{sample : total}
one part of sample in DF parts of finished mixture
sample : diluent\text{sample : diluent}
one part of sample added to DF − 1 parts of diluent

How it works

A dilution factor compares the finished volume with the volume of sample that went into it. Adding 100 µL of sample to 900 µL of diluent gives 1,000 µL, so the sample is ten times less concentrated and the dilution factor is 10.

The same dilution is written in two ways that are easy to confuse. As a dilution it is 1 : 10, one part in a total of ten. As a mixing ratio it is 1 : 9, one part of sample to nine parts of diluent. The calculator shows both so that the one on your protocol can be matched without guessing.

Worked example

100 µL of serum is added to 900 µL of saline.

  1. Final volume = 100 µL + 900 µL = 1,000 µL.
  2. DF = 1,000 µL / 100 µL = 10.

A ten-fold dilution: 1 : 10 as sample to total, or 1 part of sample to 9 parts of diluent. A result measured on the diluted sample is multiplied by 10 to report the original.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Volumes add on mixing, which holds for dilute aqueous solutions.
  • The mixture is homogeneous before anything is taken from it.

Common mistakes

  • Reading 1 : 10 as one part plus ten parts. That is an eleven-fold dilution, and the error grows with every step of a series.
  • Forgetting to multiply the measured result by the dilution factor when reporting the original sample.
  • Adding the factors of successive dilutions. They multiply: a 1 : 10 followed by a 1 : 5 is a 1 : 50.

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