Math
Confidence interval for a mean
Calculate a z-based confidence interval from a mean, standard deviation and sample size.
Calculators / Math / Sample size
Sample size calculator
Estimate a proportion survey sample size from confidence z-score, proportion and margin.
On this page
Required sample size385people
Calculator controls
How to calculate
Estimate a proportion survey sample size from confidence z-score, proportion and margin.
Required sample size = ceil(z^2*p*(1-p)/margin^2)
Worked example
Z critical value: 1.96; Estimated proportion: 0.5; Margin of error as decimal: 0.05.
Required sample size: 385 people.
Assumptions and limits
This simple random-sample formula excludes finite-population correction, design effect, nonresponse and weighting.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Estimate a proportion survey sample size from confidence z-score, proportion and margin. The displayed figures use the inputs and formula shown on this page.
When this tool is useful
Use the sample size to compare a scenario, check an estimate, or verify a manual calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Z critical value | Enter a number of at least 0.000001 and no more than 1000000000000. |
| Estimated proportion | Enter a number of at least 0.000001 and no more than 0.999999. |
| Margin of error as decimal | Enter a number of at least 0.000001 and no more than 0.999999. |
Frequently asked questions
What should I check before using the sample size result?
This simple random-sample formula excludes finite-population correction, design effect, nonresponse and weighting.
Is this sample size result exact?
It is exact for the stated mathematical model and entered values. Real-world results can differ when rates, timing, fees, definitions or measurement conditions differ.