Sample Size Formula

The sample size formula helps us find the accurate sample size through the difference between the population and the sample. To recall, the number of observation in a given sample population is known as sample size. Since it not possible to survey the whole population, we take a sample from the population and then conduct a survey or research. The sample size is denoted by “n” or “N”. Here, it is written as SS.

Learn More: Confidence Interval Formula

Sample Size Formula for Infinite and Finite Population

We should know that the sample size that we are taking from the population, will not hold good for the whole sample. We have a level of confidence and margin of error to calculate that the sample size is accurate or not. Confidence level helps describe how sure you are that the results of the survey hold true or accurate.

The sample size for an infinite (unknown) population and for a finite (known) population is given as:

Formulas for Sample Size (SS)
For Infinite Sample Size SS = [Z2p (1 − p)]/ C2
For Finite Sample Size SS/ [1 + {(SS − 1)/Pop}]


  • SS = Sample size
  • Z = Given Z value
  • p = Percentage of population
  • C = Confidence level
  • Pop = Population

Check: Z Score Table

Sample Size Formula Example

Question: Find the sample size for a finite and infinite population when the percentage of 4300 population is 5, confidence level 99 and confidence interval is 0.01?


Z = From the z-table, we have the value of confidence level, that is 2.58 by applying given data in the formula:

\(\begin{array}{l}SS=\frac{(2.58)^2\times 0.05\times (1-0.05)}{0.01^2}=316\end{array} \)

Sample size for finite population 

\(\begin{array}{l}=\frac{316}{1+\frac{316-1}{4300}}=294\end{array} \)

New SS = 294


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