How to calculate a sample size in research

Updated April 17, 2017

The sample size is the portion of a population that is included in your research. For formula purposes, the sample size is represented by the lower-case letter n, and the size of the population as a whole is indicated by upper-case N. Calculating a correct sample size will help provide you with accurate testing results. The level of precision, the level of risk and the degree of variability are all factored in to determine the best sample size for you research. To determine sample size a formula can be used combining all of this information.

Square the level of risk. Level of risk is equal to 1.96. So, 1.96x1.96 = 3.84.

Multiply 3.84 by the degree of variability times one minus the degree of variability. The degree of variability is represented by p. So, 3.84 x p(1-p).

Divide your answer from step two by the margin or error squared. Margin of error is represented by the letter m. Your equation should look like this: ( 3.84 x p[1-p]) / m^2 ). The solution will provide a sample size for a simple random sample.


A census, a sample size from a similar study or published sample size tables can also be used in determining sample size.

Things You'll Need

  • Precision level/Sampling error percentage
  • Level of risk
  • Degree of variability amount
  • Pen
  • Paper
  • Calculator
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About the Author

Reese Armstrong graduated from Kent State University in 2007 with a Bachelor of Arts in biology. Armstrong has been writing professionally since 2010 and published articles on various websites. For several years she worked as a skin care consultant for a major cosmetic company.