Sample size calculator
A 95% confidence level with a ±5% margin and no assumption about the answer needs 385 responses, whatever the population, and 384 is the figure most often quoted because of a rounding convention. It is why so many surveys land at "about 400 respondents". Assuming 50% is deliberately the worst case: any other expected proportion needs fewer.
Sample size for a proportion is z² × p(1−p) ÷ margin². At 95% confidence with a ±5% margin and no prior expectation, that is 385 responses. Regardless of population size unless the population is small.
How to work out sample size
Sample size answers only sampling error. The randomness of who happened to respond. It says nothing at all about the far larger problems of non-response bias, a badly worded question, or a sample frame that misses the people you care about. A survey of 10,000 self-selected website visitors is worse evidence than 400 properly randomised responses, and no sample size calculation will reveal that. The number here is necessary and a long way from sufficient.
Questions
385 for ±5% at 95% confidence. About 1,067 for ±3%, and 9,604 for ±1%.
Only for small populations. Above about 20,000 it makes almost no difference.
It is the worst case and needs the largest sample. Any other proportion needs fewer responses.
No. A large biased sample is confidently wrong. Sample size only addresses random sampling error.
Five per cent is common for general research; political polling often aims for three.