Sample Size Calculator
Free sample size calculator for surveys and studies. Set confidence level, margin of error and population to get the required sample size instantly.
About the Sample Size Calculator
How many people must you survey for the result to be trustworthy? This free sample size calculator answers that with the standard Cochran formula n = z² × p(1−p) ÷ e², where z depends on your confidence level (1.96 for 95%), p is the expected proportion and e is the margin of error. If you know the population size, it applies the finite population correction n ÷ (1 + (n−1)/N) to shrink the requirement.
Researchers, students designing thesis surveys, market-research teams and NGOs planning field studies in Pakistan and India all rely on this calculation before collecting data. Using p = 50% gives the safest (largest) sample when you have no prior estimate. The tool runs entirely in your browser — adjust the margin of error and watch the required sample update live.
How to Use the Sample Size Calculator
- 1Choose a confidence level — 95% is the standard for most surveys.
- 2Enter the margin of error you can accept (5% is typical).
- 3Enter the expected proportion, or keep 50% if unsure.
- 4Optionally add the population size for the finite-population correction.
Frequently Asked Questions
How is sample size calculated with an example?
For 95% confidence (z = 1.96), 5% margin of error and p = 50%: n = 1.96² × 0.5 × 0.5 ÷ 0.05² = 3.8416 × 0.25 ÷ 0.0025 = 384.16, rounded up to 385 respondents. This is the classic sample size quoted for large populations.
How does population size change the required sample?
For a population of 1,000, the finite correction turns 385 into 385 ÷ (1 + 384/1000) ≈ 278. For very large populations the correction barely matters — a city of 10 million still needs about 385. That is why national polls need only a few hundred to a few thousand respondents.
Why use 50% as the expected proportion?
The term p(1−p) is largest at p = 0.5 (0.25), so assuming 50% yields the biggest, safest sample size. If a previous study showed only 20% of people hold some view, using p = 0.2 gives p(1−p) = 0.16 and cuts the required sample from 385 to about 246 at the same precision.
What margin of error should I choose?
5% is the common default for general surveys; 3% roughly triples the sample (1,068 vs 385 at 95% confidence) and is used when decisions are sensitive. Halving the margin of error quadruples the sample because e is squared in the denominator.
Does a bigger sample fix a biased survey?
No. Sample size only controls random sampling error. If your sampling method excludes groups — say, an online-only survey missing rural respondents — the bias remains no matter how many responses you collect. Aim for a representative sampling frame first, then size it with this calculator.