Sample Size for a Proportion Guide
Sample-size planning for a proportion reverses the margin-of-error formula. When a finite population is known, the standard correction can reduce the required sample under the stated assumptions.
Method
- Choose the confidence level.
- Set the desired margin of error in percentage points.
- Enter an expected proportion, or use 50% for the conservative variance assumption.
- Optionally enter a known finite population size, then round the corrected target up.
Worked example
At 95% confidence, ±5 points and p = 50%, the large-population result rounds to 385.
For a population of 1,000, the finite-population correction lowers the target to 278.
Notes
- Finite-population correction is applied only when you enter N.
- Design effects, clustering, nonresponse and weighting can increase practical sample needs.
- The normal approximation is a planning model, not a guarantee about study quality.
Sample size planning starts with confidence, precision and an expected proportion
A proportion sample-size formula uses the selected confidence level, desired margin of error and an assumed population proportion. When no prior estimate exists, using 0.5 is conservative because it maximizes p(1-p) and therefore gives the largest required sample under the simple model.
Tighter precision and higher confidence both increase the required sample. This tradeoff should be decided before data collection rather than adjusted after seeing the results.
Apply finite-population correction only when the population is truly bounded
When sampling without replacement from a known finite population, the required sample can be reduced using a finite-population correction, especially when the planned sample is a substantial fraction of the population.
The basic formula assumes a simple random sampling framework. Clustered designs, stratification, expected nonresponse or design effects can require a larger recruitment target than the calculator's statistical minimum.
A whole-survey target may be too small for regional decisions
A shop wants to estimate the share of customers satisfied with a new checkout process. Under a simple random sampling model, a conservative planning proportion of 50%, 95% normal confidence and 400 completed responses imply an approximate margin of error of 1.96 × √(0.5 × 0.5 ÷ 400) = 0.049, or 4.9 percentage points. This is a planning illustration, not a statement about any real survey. The linked sample-size calculator reverses this idea when you enter the desired precision before recruiting participants.
Now suppose the business splits those 400 responses evenly across four regions. Each region has only 100 completed responses, and the same conservative approximation gives about 9.8 percentage points for each regional estimate. If the requirement were roughly 4.9 points in every region, the simple model would call for around 400 completed responses per region—about 1,600 in total before any design or recruitment adjustments. A company-wide sample size should not be silently reused as the precision of each subgroup.
Recruitment feasibility and bias are separate questions
A completed-response target is not the same as an invitation count. If the survey needs 400 usable responses and an independently justified planning assumption is a 40% response rate, 400 ÷ 0.40 = 1,000 invitations gives a rough recruitment budget. The response rate can be lower, and the observed respondents may differ systematically from people who ignore the invitation. Sending enough emails does not prove that the sample is representative or that the mathematical margin of error describes every survey error.
Define who is eligible, how customers are selected and whether responses are clustered by household, workplace or repeated purchase. Nonprobability opt-in polls should not present the simple random-sample confidence margin as guaranteed coverage. Before launching an expensive survey, test the questionnaire for ambiguous wording and confirm whether the decision needs one overall estimate, several subgroup estimates or a comparison between groups; those questions lead to different sampling plans.
Editorial review and limitations
Continue with the related tools
Use the linked tools for your own inputs and scenarios.
- Margin of Error Calculator — Calculate a normal-approximation margin of error for a proportion from sample size, estimated proportion and confidence level.
- Mean Confidence Interval Calculator — Calculate a normal-approximation confidence interval for a mean from the mean, standard deviation, sample size and confidence level.
- Standard Error Calculator — Calculate the standard error of a sample mean from standard deviation and sample size.