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Survey Sample Sample Size Estimator

The Survey Sample Sample Size Estimator calculates how many completed responses are needed to estimate a population proportion at a chosen confidence level and margin of error. It is intended for polls, customer surveys, employee research, market questionnaires, and other studies where the main outcome can be expressed as a percentage or proportion.

The estimator uses the standard normal approximation for a proportion and can apply a finite population correction when you provide a population size. If you do not have a prior estimate for the expected proportion, 50% is conservative because it produces the largest variance and therefore the largest required sample under this model. The result is rounded up to a whole response so the target does not fall below the calculated requirement.

Survey precision inputs

%
%
Result
—
Required completed responses
Initial sample size—
Finite-population adjusted—
Expected proportion—
Margin of error—

1. Choose confidence
Select the confidence level used to set the normal critical value.

2. Set acceptable error
Enter the maximum margin of error you want for a proportion estimate, expressed in percentage points.

3. Estimate the proportion
Provide the expected proportion. Use 50% when you have no useful prior estimate and want the conservative variance case.

4. Add population size if relevant
Enter a finite population size when sampling without replacement from a known population. Leave it at 0 to use the large-population result.

5. Use the rounded-up target
The main result is rounded upward to the next whole completed response. Account separately for expected nonresponse when deciding how many invitations to send.

Initial n = z² × p × (1 − p) / e² Finite-population n = n₀ / [1 + (n₀ − 1) / N] Required responses = ceil(adjusted n)

z is the normal critical value for the selected confidence level, p is the expected population proportion as a decimal, e is the desired margin of error as a decimal, and N is the finite population size. The finite population correction is applied only when N is greater than zero.

What the result means

The result is the minimum completed-response target under the stated normal-approximation assumptions and, when entered, the finite population correction.

Complex survey designs, weighting, clustering, stratification, and expected nonresponse can require a larger operational sample than this simple random-sample estimate.

Given: 95% confidence, 5% margin of error, expected proportion 50%, population size 10,000.

Calculation: Initial n = 1.96² × 0.50 × 0.50 / 0.05² = 384.15. Finite-population adjusted n = 384.15 / [1 + (384.15 − 1) / 10,000] ≈ 370.00.

Result: Round up to 370 completed responses.

This is the completed sample target for the precision assumptions; invitation volume should be higher if some people will not respond.

Why is 50% often used for the expected proportion?

For a binary proportion, p × (1 − p) is largest at 50%. Using 50% therefore gives the largest required sample when no better prior estimate is available.

Does population size always matter?

Not much when the population is very large relative to the sample. The finite population correction becomes more noticeable when the required sample is a meaningful fraction of the total population.

Should I increase the result for nonresponse?

Yes if you are planning invitations rather than completed responses. Divide the required completes by the expected response rate to estimate how many people may need to be contacted.

Can this formula handle cluster or stratified surveys?

Not directly. Complex designs can change variance through design effects, allocation rules, and weighting, so a dedicated survey-design calculation may be needed.

Is margin of error the same as total interval width?

No. Margin of error is the distance from the estimate to one side of the interval. A symmetric interval with a 5-point margin of error has an approximate total width of 10 percentage points.