Sample Size Calculator

Estimate a survey sample size for a population proportion using confidence, margin of error and optional finite-population correction

This estimates sample size for a proportion under simple random sampling; design effects and non-response require separate adjustment.

Your result will appear here.

About the Sample Size Calculator

Sample size planning estimates how many observations are needed to achieve a chosen precision or statistical power under specific assumptions. It helps turn a target margin of error or detectable effect into a practical data-collection requirement.

The calculation is only as good as the assumptions about variability, confidence, population size and expected proportion. A larger sample reduces sampling uncertainty, but it does not correct biased sampling or poor measurement.

How to Use the Sample Size Calculator

  1. Choose the sample-size method that matches a mean, proportion or other supported design.
  2. Enter the desired confidence level and margin of error.
  3. Enter an estimated population proportion, standard deviation or effect assumption as required.
  4. Calculate the required sample and round up to a whole observation, then allow for nonresponse or unusable data separately.

How the Calculation Works

For a proportion with a large population, n = z²p(1−p)/E², where z is the critical value, p is the expected proportion and E is the desired margin of error in decimal form.

When population size is finite, a finite-population correction can reduce the required n. Other study designs use different formulas based on standard deviation, effect size, power and group structure.

Worked example

Sample Size Calculator Worked Example

95% confidence, ±5% margin, p=0.5

Using z≈1.96, n = 1.96²×0.5×0.5 ÷ 0.05² ≈ 384.16. Round up to 385 completed observations before adding any allowance for expected nonresponse.

Result guide

Understanding Your Sample Size Calculator Result

The result is the number of usable observations required under the selected model. It is not the number of people you necessarily need to contact if some will not respond.

Before you rely on the answer

Assumptions and Limitations

  • Confidence level and margin of error are selected appropriately.
  • The assumed proportion, variance or effect size is reasonable.
  • Sampling is independent enough for the chosen formula and the design effect is not ignored when clustering matters.

Practical tip

Using This Result in Practice

If you are unsure about an expected proportion in a simple proportion survey, p=0.5 is conservative because it produces the largest variance. For real studies, also plan for response rate, eligibility losses and subgroup analyses.

Related calculations

Useful Calculations to Continue With

If you already know the sample size and want the expected precision, use the Margin of Error Calculator.

After data are collected, use the Confidence Interval Calculator to estimate a range around the sample result.

Authoritative references

Useful Official Sources

For standards, definitions or real-world guidance related to this calculation, these primary sources may be useful:

Common questions

Sample Size Calculator FAQ

Why does a smaller margin of error require a larger sample?

Greater precision requires more observations because sampling uncertainty falls roughly with the square root of sample size.

Does a huge population always require a huge sample?

Not necessarily. Once the population is large relative to the sample, required size depends more on precision and confidence than total population size.

Should I round sample size up or down?

Round up because a fractional required observation means the smaller whole number would not meet the target under the formula.