Calculate sample size, population, or margin of error with Slovin’s formula, plus rounded respondent targets, response-rate planning, and worked steps.

Required: population size and margin of error.
Known finite population; enter a whole number.
Enter the number of completed responses.
Enter as a percent, such as 5 for ±5%.
Used only to estimate invitations for the sample-size mode.
Formula used: n = N ÷ (1 + N × e²). Use e as a decimal. This quick estimate is intended for a finite population and simple random sampling without replacement.

Related Calculators

Slovin’s Formula

The following formula is used to calculate the sample size using Slovin’s formula:

n = N / (1 + N * e²)

Variables:

  • N is the total population size
  • e is the margin of error (as a decimal)
  • n is the sample size

To calculate the sample size using Slovin’s formula, divide the population size by the sum of 1 plus the population size multiplied by the square of the margin of error.

What is Slovin’s Formula?

Slovin’s formula is a mathematical formula used to calculate the sample size needed when conducting a survey or experiment. It is used to estimate the number of observations or responses needed to accurately represent a population when the population size is large and the exact number of the population is known. The formula takes into account the desired margin of error and provides a sample size that minimizes the error in the results.

How to Calculate Sample Size Using Slovin’s Formula?

The following steps outline how to calculate the sample size using Slovin’s Formula.

  1. First, determine the total population size (N).
  2. Next, determine the margin of error (e) as a percentage.
  3. Convert the margin of error to a decimal by dividing by 100.
  4. Use the Slovin’s formula: n = N / (1 + N * e^2).
  5. Finally, calculate the sample size (n).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Total population size (N) = 1000

Margin of error (e) = 5%