The purpose of dilution is to decrease the concentration of cells (or other substance of interest) in a sample to a useful level. This is done by adding a known amount of sample to a known amount of diluent, usually using a pipette.

Dilution calculations depend on five simple rules:

**Rule 1**

The dilution is the amount of sample divided by the total amount of material present.

The total amount of material present is the amount of sample plus the amount of uncontaminated material used as the diluent. Mathematically, d = x / (x + y) , where d is the dilution, x is the amount of sample diluted and y is the amount of diluent. When working with liquid samples, use volumes as the units for x and y. When working with solid samples, such as soil, use weights as the units. Assume that 1 ml of liquid diluent weighs 1 g. Note that d has no units and will always be less than one.

**Example**

1 ml of raw sewage plus 9 ml of sterile water = 1 / (1+9) dilution = 10^{-1} dilution.

1 g of soil plus 49 g (49 ml) of sterile distilled water = 1/(1+49)=1/50=2 X 10^{-2} dilution.

**Rule 2**

The final dilution in a serial dilution is the product of all the dilutions that led up to it.

In serial dilutions, a dilution of the sample is used as the source for further dilution.

**Example**

1 ml of raw sewage plus 9 ml of sterile water = 1 / (1+9) dilution = 10^{-1} dilution.

1 g of soil plus 49 g (49 ml) of sterile distilled water = 1/(1+49)=1/50=2 X 10^{-2} dilution.

**Rule 3**

To obtain the concentration in the original sample, divide the measured result by the dilution from which the result was obtained.

**Example**

1 ml of a 10^{-6} dilution of soil is plated and incubated, resulting in 78 colonies. The concentration of bacteria in the soil is estimated as 78/10^{-6} = 7.8 X 10^{7} colony forming units per gram.

A 10^{-3} dilution of egg white contains 30 ug/ml of lysozyme. The egg white contained 30/10^{-3} = 3 X 10^{4} ug/ml lysozyme.

**Rule 4**

To obtain the total amount of substance in a sample, multiply concentration by the amount of sample.

**Example**

If there are 2 X 10^{7} bacteria/g of soil, then 5 g of soil contains 5 X 2 X 10^{7}, or 10^{8} bacteria.

**Rule 5**

To estimate which dilutions to plate, use the following formula:

d = (colonies on plate)/(i X CFU ml^{-1})

The value for "colonies on the plate" is arbitrarily chosen to be between 30 and 300 and to make "d" an even power of 10. Then plate one dilution on either side of the calculated value to be sure you obtain countable plates.

**Example**

You believe you have about 2 X 10^{9} CFU/ml. You want to plate 0.1 ml. What tube dilutions should you plate?
Find a number between 30 and 300 that is evenly divisible by 10 and by 2. Possibilities are 20 (too small), 200 (just right), 2000 (too big), etc.

d = (200)/(0.1 X 2 X 10^{9}) = 10^{-6}

To ensure obtaining a countable plate, you would plate a final plate dilution of

10^{-5}, 10^{-6}, and 10^{-7}.