Sample Size for a Proportion Calculator
Estimate a sample size for a proportion from an expected proportion, margin of error and confidence z-score, with an optional finite-population correction.
How to use this calculator
- Enter p between 0 and 1, margin as a percent, z-score and optional population size.
- Confirm that all inputs use the stated units and the same population, period or scope.
- Change one assumption at a time when comparing scenarios.
Formula used by the sample size proportion calculator
n₀=z²p(1−p)/E²
- n₀=z²p(1−p)/E²
- The calculation assumes a simple random sample and does not include nonresponse or clustered-sample design effects.
- Inputs are validated against required ranges and outputs are rounded for readability.
Worked examples
Worked example
Use p=0.5, z=1.96 and a 5% margin of error.
The large-population initial estimate is about 385 observations.
The large-population initial estimate is about 385 observations.
Understanding the result
Estimate a sample size for a proportion from an expected proportion, margin of error and confidence z-score, with an optional finite-population correction.
The calculation assumes a simple random sample and does not include nonresponse or clustered-sample design effects.
Important notes
The calculation assumes a simple random sample and does not include nonresponse or clustered-sample design effects.
Use the result as a calculation aid for the inputs supplied; confirm critical specifications independently.
Frequently asked questions
Why is p=0.5 often used?
It maximizes p(1−p) and therefore gives a conservative sample size when the proportion is unknown.
Does this guarantee representativeness?
No; sampling method and response bias matter beyond sample size.
How do I use this calculator?
Enter p between 0 and 1, margin as a percent, z-score and optional population size.
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- Sample Size Calculator — Estimate a simple random-sample size for a proportion using a chosen confidence z-score, assumed proportion and margin of error.
- Margin of Error Calculator — Estimate a simple proportion margin of error from sample size, assumed proportion, and a critical z value.
- Percent Error Calculator — Calculate percentage error and absolute error between observed and reference values.
- Standard Error Calculator — Estimate the standard error of a sample mean from sample standard deviation and sample size.
- Proportion Calculator — Solve a simple proportion with three known values.
- Two-Proportion Z-Test Calculator — Compare two independent success proportions using a pooled z statistic and a two-sided normal approximation.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.