Sample Size Calculator
Find how many responses a survey needs for a chosen confidence level and margin of error.
Required sample size385
Sample size n = z² · p · (1 − p) ÷ e², where z is the confidence-level score, p is the expected proportion and e is the margin of error (both as decimals). For 95% confidence (z = 1.96), a 50% proportion and a 5% margin, n = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16, rounded up to 385 responses. Using p = 50% gives the largest, safest sample when you can't estimate the proportion in advance.
Questions
How is sample size calculated?
n = z² × p × (1 − p) ÷ e², where z is the z-score for your confidence level, p is the expected proportion and e is the margin of error. At 95% confidence with p = 50% and a 5% margin, you need 385 responses.
What proportion should I use?
If you have no estimate, use 50% — it produces the largest required sample, so your survey is never under-powered. If you expect a more extreme split (say 80/20), entering it lowers the needed sample size.
What does the margin of error mean?
It is how far your survey result may be from the true value. A 5% margin means a measured 60% could really be anywhere from about 55% to 65%. A smaller margin needs a larger sample.