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Lessons · Medicine foundations · dilutions and counting cells

Dilutions, and turning a count into a concentration

A dilution factor is the total number of parts divided by the parts of sample; a count in a known volume becomes cells per microlitre by dividing by that volume, and the dilution is then undone by multiplying back.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

In a haematology practical you count cells under a microscope and write a number on your page. That number is not what goes on the report, because the sample was watered down before you looked at it, and undoing that is a multiplication nobody can see you skip.

How to think about it

Count the parts: one part sample plus nine parts diluent is ten parts in total, so the factor is 10, not 9. Divide the count by the chamber volume to get cells per microlitre in what you looked at. Multiply by the factor to get back to the original. Diluting makes a sample weaker, so undoing it must make the number bigger.

Worked example

1 part sample and 9 parts diluent make 10 parts, a 1 in 10 dilution, so the factor is 10
Total parts over sample parts. The nine is the diluent alone and is not the factor.
120 cells counted in a chamber volume of 0.1 microlitre
The count and the volume it was counted in.
120 / 0.1 = 1200 cells per microlitre in the diluted sample
Dividing by a tenth multiplies by ten, which is why this step surprises people.
1200 × 10 = 12000 cells per microlitre in the original
Undoing the dilution. Bigger, as it must be.

Your turn

A 1 in 5 dilution was used and 90 cells were counted in 0.1 microlitre. Write the line that gives the concentration in the original sample.

90 / 0.1 × 5 =  cells per microlitre

The trap

Dividing by the dilution factor instead of multiplying by it. Diluting made the sample weaker, so the original has to come out stronger; if your answer is smaller than what you counted, the multiplication went the wrong way.

Practise dilutions and counting cells on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.