How to Calculate Sample Size for Research

Too small a sample and your study lacks the power to detect a real effect. Too large, and you've wasted time and resources. Sample size calculation is how you find the number that's actually justified by your design — not a guess, and not "as many as I can get."

What determines your required sample size

• Confidence level — how certain you want to be (typically 95%).
• Margin of error — how much imprecision you'll accept in your estimate.
• Expected variability — a proportion near 50% or a large standard deviation requires a bigger sample.
• Effect size — for hypothesis-testing studies, smaller effects require larger samples to detect reliably.
• Statistical power — typically set at 80% or 90%, the probability of detecting a real effect if one exists.

Two common approaches

For estimating a proportion or descriptive statistic: Cochran's formula, based on your desired confidence level and margin of error. Try our free Sample Size Calculator for this directly.

For hypothesis-testing or comparing groups: a power analysis, which additionally requires an expected effect size. This typically needs dedicated software (e.g., G*Power) rather than a simple formula, since the calculation differs by test type (t-test, ANOVA, regression, etc.).

Common mistakes

• Skipping the calculation entirely and using a "round number" instead.
• Using p=50% justification for a proportion you actually have prior data on (using the actual expected proportion gives a more efficient, often smaller, sample size).
• Not accounting for expected dropout or non-response, leaving the study underpowered by the end.

Committees and journal reviewers increasingly expect a documented sample size justification, not just a final number.