Sample Size Calculator
Find the survey sample size you need for a target confidence level and margin of error, with an optional finite-population correction. Uses n = z²p(1−p)/E².
Required sample size
385
n = z²·p·(1 − p) / E² = 1.96² × p(1 − p) / E²
Use p = 50% if you do not know the expected proportion — it gives the largest, safest sample size. The z value comes from an inverse-normal approximation. Sample sizes are always rounded up.
Frequently Asked Questions
How do I calculate the sample size for a survey?
Use n = z²·p·(1 − p) / E², where z is the critical value for your confidence level (1.96 for 95%), p is the expected proportion, and E is the margin of error as a decimal. Round the result up to the next whole person.
What proportion should I use if I don't know it?
Use p = 0.5. It gives the largest possible product p·(1 − p), so it produces the most conservative (largest) sample size and guarantees your margin of error is met no matter the true proportion.
What is the finite population correction?
When your population is small, the basic formula overestimates the sample needed. The correction is n_adj = n / (1 + (n − 1)/N), where N is the population size. For large populations the correction has almost no effect.
How does the margin of error affect sample size?
Sample size grows with the square of the inverse of the margin of error. Halving the margin of error (say from 5% to 2.5%) quadruples the required sample. Tighter precision is expensive.
How does the confidence level affect sample size?
A higher confidence level uses a larger z value, which increases the sample size. Moving from 95% (z = 1.96) to 99% (z = 2.576) raises the required sample by roughly 73% for the same margin of error.