Sample Size Calculator

Calculate required sample size, estimated invitations, or margin of error for survey planning

Check Sample Size Calculator

Use 50% if unknown (maximum variability)

Leave blank for large/unknown populations

Use 1 for simple random samples; use higher values for clustered or weighted samples.

Estimates invitations needed to reach the completed response target.

Try:

Formula result

Copy-ready result handoff

Use this after estimating how many observations are needed.

Common searches
sample size calculatorsurvey sample sizemargin of error
Input check

Confirm confidence level, margin of error, population size, and expected proportion.

Assumption

Finite population correction only applies when the population size is known.

Sample size planning note

Copy this after replacing the bracketed result with the value shown by the calculator.

Sample size result: [paste required sample size, margin of error, and confidence level].
Inputs checked: Confirm confidence level, margin of error, population size, and expected proportion.
Assumption: Finite population correction only applies when the population size is known.
Use case: Survey planning, experiment planning, estimate check, or research proposal.
Next check: Use Confidence Interval Calculator after data collection.

Choose whether you need a required sample size before data collection or a margin of error for a completed sample. Add finite population size, design effect, and response rate only when those values match your survey plan.

How the result is built

Formula, Variables, And Worked Example

n0 = z^2 * p * (1 - p) / E^2

z is the confidence critical value, p is the expected proportion, and E is the margin of error as a decimal.

Worked example

For 95% confidence, z = 1.96. With p = 0.5 and E = 0.05, n0 = 1.96^2 * 0.5 * 0.5 / 0.05^2 = 384.16, so round up to 385.

Assumptions and common mistakes
  • Use p = 0.5 when the expected proportion is unknown; it gives the conservative largest sample.
  • Enter margin of error as a decimal in the formula, so 5% becomes 0.05.
  • Round the final required sample size up, not to the nearest whole number.
  • Use finite population correction only when the population size is known and sampling is without replacement.
Planning inputs
  • Margin of error is the desired half-width of the final interval.
  • Design effect increases completed responses when the sample design is less efficient than simple random sampling.
  • Response rate converts completed responses into estimated invitations.
Related checks
Confidence intervalsZ-scoresStatisticsProbability

Sample Size Formula, Assumptions, And Mistakes

When to use the sample size calculator

Use this page before a survey when you need to know how many completed responses are required for a target margin of error. Use margin mode after data collection when you know the sample size and want the precision of the estimate.

How confidence level changes the answer

Higher confidence levels use larger z critical values, which increases the sample size needed for the same margin of error. Moving from 95% to 99% confidence can require many more responses, especially when the target margin of error is small.

Finite population, design effect, and response rate

Finite population correction can reduce the required sample when the total population is known and relatively small. Design effect increases the completed response target for clustered or weighted samples. Response rate estimates how many invitations may be needed to achieve the completed response count.

Connect planning to final intervals

After collecting responses, use the Confidence Interval Calculator to turn the observed result into a lower bound, upper bound, and margin of error. Use the Z-Score Calculator when you need to inspect the confidence critical value directly.

References & Sources

Common result checks

Questions about this tool

Why does the calculator suggest p = 50% when I am unsure?
A 50% expected proportion creates the largest required sample size for a proportion estimate, so it is a conservative planning value.
Should I round the sample size up or down?
Round up. A required sample size of 384.16 means you need at least 385 completed responses to meet the target margin of error.
When should I use finite population correction?
Use it when the total population size is known and the sample is a meaningful fraction of that population. Leave it blank for large or unknown populations.
What is design effect?
Design effect adjusts for sampling designs such as clustering or weighting. Use 1 for a simple random sample, and use a higher value only when your study design calls for it.