Sample Size Calculator
Calculate the number of survey responses needed for a given confidence level and margin of error, adjusted for your population size.
Example
For a 95% confidence level (z = 1.96), a 5% margin of error, p = 50%, and a population of 10,000:
n0 = z² · p(1−p) / e²
= 1.96² · 0.5·0.5 / 0.05²
= 3.8416 · 0.25 / 0.0025
= 384.16 -> 385 (infinite population)
Finite population correction (N = 10,000):
n = n0 / (1 + (n0−1)/N)
= 384.16 / (1 + 383.16/10000)
= 369.98 -> 370 responses
How it works
Enter your confidence level, margin of error, population size and expected response proportion; the tool applies n = z²·p(1−p)/e² and the finite population correction. It rounds up to the next whole respondent so your margin of error is met.
Good to know
The Sample Size Calculator tells you how many completed survey responses you need so your results carry a chosen level of statistical confidence at an acceptable margin of error. It is built for anyone running a poll, customer survey, market study, A/B audience test or academic questionnaire who needs a defensible target before fielding, rather than guessing at a round number like "100 people."
Use it when you are planning the study, not after. Set your confidence level (how often a repeated survey would land inside the margin), your margin of error (the +/- band you can tolerate around each percentage), the size of the group you are sampling from, and an expected response proportion. The output updates instantly as you type, so you can trade off precision against cost: tightening the margin from 5% to 3%, or moving from 95% to 99% confidence, both push the required sample up sharply.
Read the headline number as the count of finished responses you must collect, already rounded up so the stated margin is genuinely met. The "Uncorrected" figure is the same calculation assuming an unlimited population, so seeing it sit higher than the headline tells you the finite population correction actually saved you responses. The "Response rate buffer" estimates how many invitations to send assuming roughly 30% reply, a quick reality check on outreach volume.
- Completes are not invites: the headline is responses received, while the buffer is the larger pool of people you must contact.
- The math assumes a random, representative sample; a large sample drawn from a biased frame is still biased, just precisely so.
Frequently asked questions
Why does response proportion default to 50%?
p = 50% maximizes p(1−p), which gives the largest (most conservative) sample size. When you do not know the expected split, using 50% guarantees your margin of error is met regardless of the true proportion.
When does the finite population correction matter?
It only shrinks the sample meaningfully when your population is small relative to the uncorrected size. For very large or unknown populations, leave population blank and the tool uses the standard infinite-population formula.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is a good sample size for a survey of 1000 people?
At 95% confidence and a 5% margin of error with an unknown response split, you need roughly 278 completed responses from a population of 1,000. Tightening the margin to 3% raises that to about 517, so the right number depends on the precision you require.
What's the difference between confidence level and margin of error?
Confidence level is how often a repeated survey would produce a result inside your error band, such as 95% of the time. Margin of error is the size of that band, for example +/- 5 percentage points around a reported figure.
Does a bigger population always require a bigger sample?
No. Beyond a few thousand people, the required sample barely grows, which is why national polls of millions still use only about 1,000 to 1,500 respondents. The finite population correction only reduces the sample meaningfully when the population is small relative to the uncorrected number.
How do I account for survey non-response when choosing a sample size?
Decide how many completed responses you need, then divide by your expected response rate to get the number of invitations to send. For example, 370 completes at a 30% response rate means inviting roughly 1,234 people.
What confidence level and margin of error should I use?
95% confidence with a 5% margin of error is a common general-purpose default. Use 99% confidence or a smaller margin for higher-stakes decisions, accepting that both significantly increase the sample you must collect.
Can I use this calculator for proportions other than 50%?
Yes. If you have prior data suggesting the result will be far from a 50/50 split, entering that proportion lowers the required sample because p(1-p) shrinks. If you are unsure, 50% is the safe, most conservative choice.
What does Z-score mean in a sample size calculation?
The Z-score is the number of standard deviations corresponding to your confidence level under a normal distribution. It is about 1.64 for 90%, 1.96 for 95%, and 2.58 for 99%, and it enters the formula as z squared.
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