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

Enter the known population and the model error target.

Planning heuristic for a finite population, simple random sampling without replacement and a population proportion. It does not guarantee representativeness or a measured confidence interval.

Enter a percentage greater than 0 and less than 100.

Response-rate planning

Optional assumption for invitation planning; not a response guarantee.

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 sample-size planning heuristic for estimating a population proportion from a known finite population under simple random sampling without replacement. Its usual derivation assumes a proportion near 0.5 and uses z ≈ 2, corresponding approximately to 95% confidence under those assumptions. It does not guarantee representativeness, calculate an achieved confidence interval or minimize all survey errors. Use a study-specific sample-size or power method for other outcomes, experimental designs or sampling designs.

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 Slovin’s formula: n = N / (1 + N * e^2).
  5. Finally, calculate n and round upward to a whole completed-response target within the model.
  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%

Convert 5% to 0.05: n = 1000 / (1 + 1000 × 0.05²) = 285.714285… . Round upward to 286 completed responses under the model assumptions.