The formula
The dilution factor is how many times more dilute the sample has become:
dilution factor = total volume ÷ sample volume = starting concentration ÷ final concentration
10 µL of sample made up to 100 µL with buffer is 100 ÷ 10 = a dilution factor of 10. Diluting a 5 mg/mL stock to 0.5 mg/mL is also a factor of 10.
What 1:10 means
Written as a ratio, 1:10 usually means 1 part sample in 10 parts total (factor 10), but some people read it as 1 part sample plus 10 parts diluent (factor 11). The two differ by 10%. Protocols that say "1 in 10" or "10-fold" are unambiguous; when you write one, give the volumes.
Serial dilutions multiply
In a serial dilution each step is made from the previous tube, and the factors multiply. Three 1:10 steps give 10 × 10 × 10 = 1,000, written 10−3. Two 1:2 steps and one 1:5 step give 2 × 2 × 5 = 20. This is how a 1:1,000,000 dilution is made accurately without pipetting a microlitre into a litre.
Going back to the original
Multiply what you measured by the total dilution factor. A plate from the 10−4 tube with 120 colonies from 100 µL means 120 ÷ 0.1 mL × 10,000 = 1.2 × 107 cfu/mL in the original culture. On a hemocytometer, cells mixed 1:1 with trypan blue have a factor of 2, and a sample diluted 1:5 before that has a total factor of 10.
Finding the volumes for a target factor
For a factor F in a final volume V, use V ÷ F of sample and the rest diluent. A 1:40 dilution in 200 µL is 5 µL of sample and 195 µL of buffer. Factors above about 20 in one step mean pipetting tiny volumes, so split them into two steps.
Calculators
The Dilution Calculator solves C1V1 = C2V2 for any one of the four values. The Serial Dilution Calculator plans the tubes and volumes for a series, and the Hemocytometer Calculator applies the dilution factor to a cell count.