Sample Size Calculator

Sample size (n) is the minimum number of respondents or observations needed for survey results to be representative of the entire population with a specified accuracy and confidence level. A larger sample reduces the margin of error but increases cost and time.

The basic formula is n = (z^2 * p * (1-p)) / e^2, where z is the normal distribution quantile for the chosen confidence level, p is the expected proportion, and e is the acceptable margin of error. The result is rounded up to the nearest integer.

A 95% confidence level means that if the study were repeated many times, 95% of the resulting confidence intervals would contain the true population parameter. Social and market research typically uses 95%; scientific and medical research often requires 99%.

The margin of error e is the maximum acceptable difference between the sample result and the true population parameter. For example, e = 0.05 means the result may differ by at most 5 percentage points from the true value. A smaller margin of error requires a larger sample.

When the expected proportion is unknown, use p = 0.5. This is the conservative worst-case scenario because p*(1-p) is maximised at 0.25, producing the largest possible sample size and ensuring adequate precision regardless of the true proportion.

The basic formula assumes an infinite population. When the population size N is known, apply the correction: n_adj = n*N / (n+N-1). This reduces the required sample size. The correction makes a significant difference when N is small relative to the uncorrected n.

For large populations (millions), the required sample is almost the same as for a population of 10,000. Sample size depends primarily on the desired precision (e), not on population size. The finite population correction only matters when N is relatively small.

For national surveys, a typical sample is 1,000-1,500 with e=3% at 95% confidence. For local or segment research, 300-500 may suffice. The calculator gives the statistical minimum; in practice, you should account for non-response and sampling method.

The sample size formula assumes random sampling where each element has an equal chance of selection. Non-random sampling methods (convenience, purposive) do not allow statistical guarantees of representativeness; the formulas do not apply to them.

A smaller margin of error means greater precision, but also a significantly larger sample and higher costs. Reducing e from 5% to 3% roughly quadruples the required sample size. The choice of margin of error should reflect the practical requirements and budget of the study.