How this calculator works
For a normal confidence margin, square the ratio of the critical-scaled variability to the target margin. For proportions, p = 0.5 maximises the binomial variance and is conservative when no estimate is available. A finite population reduces the requirement under simple random sampling without replacement. Round upward so the planned margin is no larger than requested. These are planning approximations, not guarantees for a biased or complex survey design; inflate separately for non-response or clustering.
Formula
Mean n0 = z²σ²/E². Proportion n0 = z²p(1 - p)/E². Finite-population n = Nn0/(N - 1 + n0); round up.
Worked example
For 95% confidence, p = 0.5 and a 5-percentage-point margin, n0 ≈ 384.146 and the required sample is 385. From a finite population of 1000, the corrected requirement is about 277.74, rounded to 278.
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Frequently asked questions
Is this a power calculation?
No. It targets precision of an estimate. Detecting a specified difference requires alpha, power and an effect size.
What if the final response rate is 80%?
Divide the required completed sample by 0.8 and round upward to plan invitations, provided the non-response assumptions are reasonable.
Can I use p = 0 after observing no events?
An endpoint planning value would give a false zero-variance requirement. Use a justified non-zero planning estimate or 50% conservatively.