Sample Size Calculator
Survey sample size needed for a target margin of error and confidence.
Required sample size
385
95% confidence, ±5%
z-value
1.96
Population
infinite
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How the Sample Size Calculator works
The Sample Size Calculator tells you exactly how many survey respondents you need to achieve a target margin of error at a chosen confidence level, saving you from costly over-sampling or misleading under-sampling. It's built for researchers, pollsters, marketers, and students who need statistically defensible results from surveys or experiments.
At its core, the calculator solves for the minimum number of completed responses required so that your survey results reflect the true population value within a specified margin of error. You supply three inputs: the population size (how many people the survey is meant to represent), your desired confidence level (commonly 90%, 95%, or 99%), and your acceptable margin of error (often ±3% or ±5%). The tool then returns the sample size n that satisfies all three constraints simultaneously.
The confidence level controls how often your interval would capture the true population parameter if you repeated the survey many times. A 95% confidence level—the most widely used standard in polling and academic research—means that 95 out of 100 independent samples drawn the same way would produce an interval containing the true value. Choosing 99% confidence demands a larger sample because you are tolerating less uncertainty, while 90% allows a smaller sample at the cost of less certainty. The margin of error sets the half-width of that interval: a ±3% margin on a 60% survey result means you can report that the true figure lies between 57% and 63%.
Population size matters most when your target group is small. For very large or effectively infinite populations (generally above 100,000), the required sample size plateaus and barely changes—a national poll of 330 million Americans needs roughly the same sample as one targeting 500,000 city residents, all else equal. But for small populations—say, 800 employees in a company—the finite population correction factor significantly reduces the required n, so always enter your actual population rather than leaving it at the default infinite value. The assumed proportion (p) also plays a role: using p = 0.5 is the conservative default because it maximizes variance and therefore sample size, ensuring your results are valid even if the true split is unknown.
A common mistake is confusing the sample size needed with the number of people you must contact. Survey response rates in practice range from under 10% for cold email surveys to 60–70% for engaged panels, so you must divide your required completed-response count by the expected response rate to get your outreach target. Another frequent error is applying a sample size calculated for one subgroup to the entire study when you actually need to analyze multiple segments (age groups, regions, etc.) separately—in that case, each subgroup needs to independently meet the minimum sample size, which multiplies your total data collection effort considerably.
Formula
n = z²·p(1−p) / e² (with finite-population correction)
Pro tips
- Always use p = 0.5 when you have no prior data on the proportion you're measuring—it gives the largest (most conservative) sample size and protects you from underestimating your needs.
- For subgroup analysis, calculate sample size requirements separately for each subgroup you intend to report on independently; a nationally representative sample of 385 is rarely large enough to draw conclusions about a 10% demographic slice.
- If your population is under 10,000, always enter the exact population figure rather than treating it as infinite—the finite population correction can reduce your required sample by 20–40%, saving significant time and money.
- Work backward from your budget: enter the number of responses you can realistically collect and see what margin of error that buys you at 95% confidence—this honest trade-off conversation is more useful than chasing an unaffordable ideal sample size.
- Boost your effective sample quality by stratified sampling (dividing the population into meaningful strata and sampling each proportionally) rather than simply increasing raw numbers, which improves precision without always requiring a larger total sample.
Key terms
- Margin of Error
- — The maximum expected difference between your survey result and the true population value, expressed as ±percentage points (e.g., ±3%).
- Confidence Level
- — The probability, expressed as a percentage, that repeated samples drawn by the same method would produce intervals that contain the true population parameter.
- Z-Score (Critical Value)
- — The number of standard deviations corresponding to a chosen confidence level—1.645 for 90%, 1.96 for 95%, and 2.576 for 99% confidence.
- Population Proportion (p)
- — The estimated fraction of the population expected to answer 'yes' or hold a given characteristic; using 0.5 is the conservative default that maximizes required sample size.
- Finite Population Correction (FPC)
- — An adjustment applied when the sample represents a non-trivial share of a small population, which reduces the otherwise overestimated sample size requirement.
- Response Rate
- — The proportion of people contacted who actually complete the survey, which determines how many individuals you must invite to achieve your target completed-response count.
