About the Sample Size Calculator
Before running a survey, it helps to know how many responses you actually need for the results to be statistically meaningful, guessing too low undermines your confidence, and guessing too high wastes time and money. Our Sample Size Calculator finds the minimum required sample size from your desired confidence level and margin of error.
How It Works
You select a confidence level (90%, 95%, or 99%), specify your desired margin of error, and optionally provide a known population size and expected proportion. The calculator applies the standard sample size formula, with a finite population correction applied automatically when a population size is given.
Formula & Methodology
The core formula balances three factors: the z-score for your chosen confidence level (how many standard deviations wide your confidence interval needs to be), the expected proportion p (how the responses are likely to split), and the margin of error e (how much sampling error you're willing to tolerate). A 50% expected proportion is used by default because p(1−p) is maximized exactly at p = 0.5, making it the most conservative assumption and guaranteeing the calculated sample size is large enough regardless of how the true proportion actually splits. When the total population is small and known, a finite population correction shrinks the required sample size, since sampling a larger share of a small population yields more information per respondent than the same sample size would from an effectively infinite population.
Step-by-Step: Calculating It By Hand
- 1Look up the z-score for your chosen confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%).
- 2Convert your margin of error and expected proportion to decimals.
- 3Compute n₀ = z² × p × (1−p) ÷ e².
- 4If you know the total population size, apply the finite population correction to reduce n₀ down to the final required sample size.
- 5Round the result up to the next whole number, since a fractional respondent isn't possible.
Examples
Unknown population
At 95% confidence, a 5% margin of error, and a 50% expected proportion: the required sample size is 385 respondents.
Known small population
That same scenario applied to a population of just 1,000 people shrinks the required sample down to about 278, thanks to the finite population correction.
Advantages
- Applies the standard, widely used sample size formula automatically
- Includes an optional finite population correction for smaller, known populations
- Defaults to the most conservative expected proportion when you're unsure
- Rounds up appropriately, since sample sizes must be whole numbers
Common Mistakes
- Assuming a larger population always requires a proportionally larger sample, when in fact required sample size grows much more slowly than population size
- Guessing an expected proportion far from 50% without good evidence, which can under-power a survey if the guess is wrong
- Forgetting to apply the finite population correction when the target population is small and known
- Confusing margin of error with confidence level, they answer different questions about precision and certainty
Edge Cases to Watch For
- Margin of error must be greater than zero, since a zero margin would require an infinitely large sample.
- A population size of 0 is treated as effectively infinite or unknown, skipping the finite population correction.
- A higher confidence level always requires a larger sample size, all else being equal, since it demands a wider margin of certainty.
- An expected proportion far from 50% reduces the required sample size, but only if that assumption turns out to be accurate.
Common Use Cases
- Planning market research or customer satisfaction surveys
- Academic research requiring a statistically defensible sample size
- Political or opinion polling design
- Quality assurance sampling plans for a known batch or population size