Sample Size Calculator

n = z² · p̂(1 − p̂) / E², where z is the critical value for your confidence level and E is the margin of error. Round the answer up to the next whole number.

p̂(1 − p̂) is largest when p̂ = 0.5, so 0.5 gives the biggest — safest — sample size. If you have a prior estimate, use it and you will need fewer observations.

n = (z · σ / E)², where σ is your estimate of the population standard deviation and E is the margin of error. Round up, since you cannot collect a fraction of an observation.

Because 384.16 observations is impossible, and 384 is too few to hit the margin of error. The ceiling — 385 — is the smallest whole sample that actually meets the requirement.

Yes. A 99% confidence level uses z = 2.576 instead of 1.96, and the critical value is squared in the formula — so 99% confidence needs about 73% more observations than 95% for the same margin of error.