# How to calculate dilution factor and CFU? - (May/05/2014 )

Dear all,

I am confused regarding the calculation of dilution factor. As far as I know, dilution factor = volume of sample/total volume and CFU = (#colony x dilution factor)/volume plated in mL.

For example, if I added 1g of sample into 9mL of broth - 10^-1, and transfer 1mL from 10^-1 to second tube (9mL as well). Then this will be 10^-2.

Thus, if 1000mL of sample in tube 11 plated onto the agar and I obtained 30 colonies in this plate, CFU = (30 x 10^-11)/1000mL

Well, now came to my confusion part,

What if I added 1g of sample directly to 99mL of broth, what is the dilution factor here? According to formula it will be 1/100mL or 10^-2? But 100mL is equivalent to 11 tubes of 9mL broth, so if look at this way, it will be 10^-11 instead of 10^-2?

Please advice.

Thank you.

Correct this far.Dear all,

I am confused regarding the calculation of dilution factor. As far as I know, dilution factor = volume of sample/total volume and CFU = (#colony x dilution factor)/volume plated in mL.

For example, if I added 1g of sample into 9mL of broth - 10^-1, and transfer 1mL from 10^-1 to second tube (9mL as well). Then this will be 10^-2.

Thus, if 1000mL of sample in tube 11 plated onto the agar and I obtained 30 colonies in this plate, CFU = (30 x 10^-11)/1000mL

Where you have it wrong is that in your dilution series you are taking 1/10th EACH time you dilute, so from your initial 1 g, at the next step you are taking 0.1 g to the new tube, and the next 0.01 g and the next 0.001 g and so on.Well, now came to my confusion part,

What if I added 1g of sample directly to 99mL of broth, what is the dilution factor here? According to formula it will be 1/100mL or 10^-2? But 100mL is equivalent to 11 tubes of 9mL broth, so if look at this way, it will be 10^-11 instead of 10^-2?

Please advice.

Thank you.

Thanks for your reply. Btw, if we following the formula,

CFU= (#colony x dilution factor)/volume plated in mL

If I obtained 30 colonies from second dilution tube (10^-2),

Thus, CFU= (30x 10^-2)/1mL,

= 30 x 10^-2 CFU/mL

May I know is the calculation method get wrong? How come the answer is 30 x 10^-2 (0.3) instead of 30x10^2?

Thank you.

Its usually the inverse of the dilution factor as you have written it, so in your answer it would be 30 x10^2

Thanks for your reply. Btw, if we following the formula,

CFU= (#colony x dilution factor)/volume plated in mL

If I obtained 30 colonies from second dilution tube (10^-2),

Thus, CFU= (30x 10^-2)/1mL,

= 30 x 10^-2 CFU/mL

May I know is the calculation method get wrong? How come the answer is 30 x 10^-2 (0.3) instead of 30x10^2?

Thank you.

forget formulas!

This is how people make so many mistakes!

Use common sense and think about it, its all very logical!

If you have 30 colonies on a plate and you have a 10^-2 dilution than you have 30 colonies for that dilution (+ you have to take into the account the amount you placed on your plates)

An example:

1 ml to 9 ml (10^-1 solution) , then from this sample 1 ml to another 9ml , thus you have a 10^-2 dilution in your second dilution/tube.

If you than plate out 1ml of this sample (from the second tube/dilution) in a plate you have: 1 plate with 1ml of a 10^-2 dilution.

If you then have 30 colonies, you thus have: 30 colonies/1ml from a 10^-2 diluted sample.

Meaning: 30 colonies for 1ml => 300 colonies in total for 10 ml (whats in your 10^-2 tube) , meaning for 10^-1 its 3000 and for 10^0 its 30.000 colonies in 10 ml.

or 3000 colonies for 1 ml of the original solution.

its the same as your formula, but logic is easier and you don't need to remember formulas for it.

Using (blindly) a formula makes no sense and has no value.....

If you understand the reasoning behind the formula you will never make mistakes...

Thanks for all the explanations. I still have one more question on it,

I was added 1g of sample to 99mL to make it become 10^-2, after that I transferred 1mL from this bottle to 9mL of broth, serial dilution was performed until it came to 10^-10 (8th tube). The CFU obtained was 2.

However,

When I added 1g of the same sample to 9mL broth (to make the initial dilution factor become 10^-1) and followed by serial dilution until 10^-10 (9th tube). The result obtained was 8764.

Both are the same dilution factor, how come the results are so big different?

Thank you.

Thanks for all the explanations. I still have one more question on it,

I was added 1g of sample to 99mL to make it become 10^-2, after that I transferred 1mL from this bottle to 9mL of broth, serial dilution was performed until it came to 10^-10 (8th tube). The CFU obtained was 2.

However,

When I added 1g of the same sample to 9mL broth (to make the initial dilution factor become 10^-1) and followed by serial dilution until 10^-10 (9th tube). The result obtained was 8764.

Both are the same dilution factor, how come the results are so big different?

Thank you.

very simple answer: you have problems with making dilutions.

Making dilutions is something that many many people do wrong (or underestimate). IN some companies new people have to "train" on this for 1-2 weeks... Just to do it correctly...

You mixed it well? Especially when adding 1 gr to 99ml ...

Other reasons: the start sample was not correct (there can be a huge difference between "samples" (the powder form) if its not mixed well..

I don't know the details about your samples, but it could be a reason.

Also: a CFU of 2 is too low to take into account, its not enough, you need to be between 30-100 (something like that). 2 means nothing: it can be 2, 1, 0, 4 or 5... 2 is too low

Its btw better to start with 1 gram in 9ml and than dilute more...

But is it possible to make the dilution start with 1g to 99mL? If in this case, it seems to be less accurate. How can I increase the accuracy if I really want to use 99mL? Thanks.

But is it possible to make the dilution start with 1g to 99mL? If in this case, it seems to be less accurate. How can I increase the accuracy if I really want to use 99mL? Thanks.

As I already said: yes its less accurate.

And is it possible to do? you can do it, but its less accurate...

I am not sure why you want to skip 1 step of diluting...

Why is it so important to use 99ml right away?

In addition to Pito's comments - If you want to do 1:100 dilutions you don't have to use 99 ml and 1 g, you can use 9.9 and 0.1 g if you want to. Note also that 1 g doesn't necessarily equate to 1 ml, solute volume could be playing a part here!!!

Like Pito said, the difficulty is error - measuring 99 ml by most methods is not very accurate, for example a standard glass 100 ml measuring cylinder has an error of +/- 1 ml at STP. You could use a volumetric flask for 100 ml (+/- 0.01 ml if used properly) and weigh out 1.01 g. Similarly if you do multiple measurements of say 25 ml lots (e.g. disposable serological pipette error +/- 3% or 0.75 ml at 25 ml) then the errors are additive 0.75 +0.75+0.75 +0.75 = +/- 3 ml...

However, if you just add a single volume to a tube - then the error is a single value and there is inherently less error in measuring 10 ml than there is in 100 ml because the graduations are finer - hence the repeated dilutions are more accurate than the single larger one.