Sample Size Calculator
Determine the required sample size for surveys and experiments based on confidence level and margin of error.
| Confidence | MOE 1% | MOE 3% | MOE 5% | MOE 10% |
|---|---|---|---|---|
| 90% | 6,765 | 752 | 271 | 68 |
| 95% | 9,604 | 1,067 | 384 | 96 |
| 99% | 16,590 | 1,843 | 664 | 166 |
Work out the minimum number of survey respondents or experiment subjects needed to estimate a proportion or mean within a chosen margin of error and confidence level.
How Sample Size Calculator Works
For estimating a proportion, the formula is n = z² × p̂(1−p̂) / E², where z is the critical value matching your chosen confidence level, p̂ is your expected proportion (0.5 is the most conservative choice when the true proportion is unknown, since it maximizes the p̂(1−p̂) term), and E is your desired margin of error expressed as a decimal.
If you supply a finite population size, a finite population correction shrinks the required sample: n_adjusted = n×N / (n+N−1) — reflecting that surveying a small, fixed population needs proportionally fewer respondents than an infinite or very large one to achieve the same precision.
For estimating a mean instead of a proportion, the formula switches to n = (z×σ/E)², based on a known (or estimated) population standard deviation σ — appropriate for continuous variables like height, income, or test scores rather than a simple yes/no split.
See It In Action
Who Uses Sample Size Calculator and Why
- Determining the minimum number of survey respondents needed to estimate a proportion within a target margin of error.
- Planning how many subjects a research study needs to estimate a continuous mean, like average spending or test score.
- Adjusting a required sample size downward for a small, known population using the finite population correction.
- Comparing how tightening the margin of error changes the required number of respondents before finalizing a survey budget.
Mistakes to Avoid
- Not using the conservative p̂=0.5 assumption when the true proportion is genuinely unknown — this is the value that maximizes the required sample size and is the safe default absent better information.
- Entering the margin of error as a whole percentage number (like 5) instead of its decimal form (0.05) as the formula requires.
- Using the Proportion formula for a continuous outcome (like average income) when the Mean mode, which needs a standard deviation instead of a proportion, is the correct one.
Tips for Best Results
- Because margin of error is squared in the denominator, cutting it in half roughly quadruples the required sample size — budget for this before committing to a tight margin.
- Apply the finite population correction whenever your population size is small relative to the calculated sample size — a common rule of thumb is under about 20 times larger.
Fixing Common Problems
The required sample size seems unreasonably large. — Check your margin of error — a tighter margin dramatically increases the required sample size since E is squared in the formula's denominator. Also confirm whether p̂=0.5 (the conservative default) is really appropriate for your survey.
Terms Explained
Margin of error: The desired precision of the estimate, expressed as a decimal (E) — a smaller value demands a larger sample size.
Finite population correction: An adjustment (n_adjusted = n×N / (n+N−1)) that reduces the required sample size when surveying a small, known total population rather than an effectively infinite one.