Sample Size Calculator

How to use

1. 1Pick a mode. Proportion is for percentage estimates (survey yes/no), Mean is for continuous measurements (height, time, money), and Margin of error is the reverse calculation from a fixed sample size.
2. 2Choose the confidence level. 95% is the standard for survey research and uses z = 1.96; the row of preset chips covers 80, 85, 90, 95, 99, and 99.9 percent, and Custom accepts any value between 0 and 100 percent.
3. 3Enter the inputs. In Proportion mode, the expected proportion defaults to 50 percent for the most conservative result and the margin of error is in percentage points. In Mean mode, enter the estimated standard deviation and the desired margin in the same units.
4. 4Optionally enter the population size. Leave it blank for very large or unknown populations; supply it to activate the finite population correction, which lowers the required sample size when N is small.
5. 5Read the headline number. The required sample is always rounded up. The sensitivity table shows how the answer changes if you loosen or tighten the margin of error.
6. 6Click Copy summary to grab a one-line description with the inputs, the critical z value, and the result, ready to paste into a study protocol, an A/B test brief, a lab report, or a chat message.

About this tool

Sample Size Calculator answers the two questions every survey designer, A/B tester, and field researcher hits when they start a study. The first question is how many respondents or measurements are needed to estimate a value within a given margin of error, and the second is the reverse: given a sample you already have, what margin of error does that buy at the chosen confidence level. The Proportion mode uses Cochran's formula n = z² × p × (1 − p) / e², which is the standard textbook formula for percentage estimates and is what every published sample size calculator computes; it accepts an expected proportion p (default 50% for the most conservative result), a margin of error e in percentage points, and an optional population size N that activates the finite population correction n = n0 / (1 + (n0 − 1) / N) for surveys aimed at a small known group such as employees, students, or registered users. The Mean mode uses the normal approximation n = (z × σ / e)², where σ is your best estimate of the standard deviation of individual measurements and e is the desired margin of error in the same units. Both modes round up to the next whole respondent or measurement, because you cannot sample 384.16 people. The Margin of error mode does the reverse calculation: it takes a fixed sample size and returns the achievable margin at the chosen confidence level, also accepting an optional population to back out the finite population correction. The critical z value is derived from Peter Acklam's rational approximation of the standard normal inverse CDF, accurate to about 1.15 × 10⁻⁹ in the body of the distribution, so common choices match published values to four decimal places (95% gives ±1.9600, 99% gives ±2.5758, 90% gives ±1.6449). A built-in sensitivity table shows how the required sample grows or shrinks as the margin of error tightens, which is how field teams decide whether to push for ±3% or settle for ±5%. Step-by-step working is shown next to every result so the calculation can be copied into a methodology section, a stats homework page, a clinical trial protocol, or a marketing brief. Useful for survey design, A/B test planning, opinion polling, customer research, clinical trials, quality control sampling, field studies, election polling, market research, academic statistics homework, and any moment you need a defensible answer to "how many do we need?" Everything runs locally in your browser; nothing you type is uploaded.

Free to use. Works in your browser. No signup, no login.