How to calculate NNT without a calculator

An easy way to understand and calculate NNT

What is NNT ?

NNT represents a number of patients that need to treat one patients.
This is one of the most impressive indicators of EBM.
It makes us easy to explain the magunitude of RCT to other person by NNT.
Though it is not easy to calculate a NNT.
We need a pen and a paper or a PC or a calculator.
In this short report, I try to make calculation of NNT easier and understandable.

the standard way of calculation of NNT

Imagine you have a RCT and you want to calculate a NNT.
For example, like this↓.

Then you will begin to calculate according to a text book like `User Guides to the Medical Literature (JAMA)` .


Step1) calculate the ratio of incidence of disease ( two division )


Control group 13/202, intervention group 9/198


Step2) calculate the difference of those ratio (one subtraction)　


(13/202)-(9/198)　


This is absolute risk reduction(ARR).


Step3) calculate the inverse of ARR (one division)


1/(13/202)-(9/198)


The answer of step 3 is NNT. In this case, the NNT is 53.


To calculate one NNT, you must do three divisions and one subtraction.
Moreover, these divisions are fairly heavy!
You must use a calculator or a PC and sometimes you need some memo...

Let`s use `percentage`!!

I recommend my students to calculate NNTs via percentage.


Step1) calculate the percentages of incidence of both groups　


13/202=6.44%
9/198=4.55%


(Yes! we must devide tow times..)
It is just percentages!
The results (6.44% and 4.55%) are so easy to understand!


Step2)Calculate the difference
The difference of these number is 6.44-4.55=1.89%.
The treatment group show some effect compared to comparison group.


Step3)From ARR to NNT
This 1.89% means ARR.
So the reverse number means NNT.
NNT = 100/1.89 = 53


Can you understand?

% is akin to NNT!

The one reason why we can easy to understand `percentage` is that we fix the size of sample to 100. When we use NNT, we must fix the number of incidence of disease to 1.
To this point(fix one parameter), percentage and NNT is similar indicator but the difference where we fix the number makes NNT is uneasy to understand.

This may be better?

X　and Y are variable numbers.

Many papers presents incidence of disease in percentage.
In that case, we can calculate NNT by just one subtraction and one division.
If the difference of outcome is 2%, it means 2 persons per 100 are different.
This means 2/2, 100/2 →1 person per 50 is different .
So the NNT is 50.


If a paper do not presents percentage, we must calculate by ourselves.
The incidence of disease in both group are very important number in clinical location.

calculate the approximation of NNT without calculator

Additionally, let me introduce the most easy way of calculate the approximation of NNT.


Step1) calculate the difference of incidence of disease (one distraction)
13-9=4


step2) change the sample size in easy number to calculate
In this case let me change 202 and 198 to both 200.


Step3) divide your own sample size by difference of incidence of disease
(from step1)


200/4=50


Now you can very easily get the approximation of NNT.
With this technique, you can read papers anywhere without NNT calculators.
This way of calculation is so fast and easy!
I think this approximation of NNT is fairly useful.
Though the problem of this calculation is error. Error arises inevitably in this way of alculation.
We can not use the number as a formal NNT.
When the difference of sample size between control group and intervention group is big, the error is also big.In such case, please calculate NNT with formal way of calculation.

(I reported this contents at the 10th UK Workshop in Teaching and Practicing EBM.)


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Nobumasa Takagaki
Gastroenterologist , Kyoto, Japan
nobukin555@gmail.com