How many responses you need for a given confidence level and margin of error
Set your confidence level, target margin of error and (optionally) the population size to find the number of survey responses you need. The result updates as you change the inputs.
n = z²·p·(1−p) ÷ e², with a finite-population correction when a population size is given.
Three things drive how many responses you need. A higher confidence level (e.g. 99% instead of 95%) requires a larger sample. A smaller margin of error requires a much larger sample — halving the margin roughly quadruples the sample. The expected proportion matters too: 50% is the most conservative assumption and gives the largest sample, which is why it is the usual default when you have no prior estimate.
For estimating a proportion, the base sample size is n₀ = z² · p · (1 − p) ÷ e², where z is the critical value for your confidence level, p is the expected proportion, and e is the margin of error (as a decimal). If you know the total population size N, the finite-population correction reduces this to n = n₀ ÷ (1 + (n₀ − 1) ÷ N). The result is always rounded up to a whole number of respondents.
At 95% confidence (z ≈ 1.96), p = 50% and a 5% margin: n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² ≈ 385. With no population limit, you need about 385 responses — the well-known rule of thumb for national surveys.
The number above is how many completed responses you need. To plan how many people to invite, divide by your expected response rate — if you expect 20% to respond and need 385 completes, you should contact roughly 1,925 people.
It depends on your confidence level, margin of error and population. For 95% confidence and a 5% margin, about 385 completed responses is enough for a large population.
Use 50%. It maximises p·(1−p) and therefore gives the largest, safest sample size.
For large populations the finite-population correction barely changes the result. It matters when your population is small relative to the sample — then it can reduce the required sample noticeably.