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

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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?

Thank you.

-Celz-

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

Correct this far.

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?

Thank you.

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.

-bob1-

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.

-Celz-

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

-bob1-

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...

-pito-

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.

-Celz-

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...

-pito-

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.

-Celz-

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?

-pito-

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.

-bob1-
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