Sample Size Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Quick reference
Sample size for a large population (50% response):
| Margin of error | 90% conf. | 95% conf. | 99% conf. |
|---|---|---|---|
| +/-5% | 271 | 385 | 664 |
| +/-3% | 752 | 1,068 | 1,843 |
| +/-2% | 1,691 | 2,401 | 4,147 |
| +/-1% | 6,764 | 9,604 | 16,588 |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
What changes the required size:
| Lever | Effect |
|---|---|
| Lower margin of error | Needs a larger sample |
| Higher confidence | Needs a larger sample |
| Response near 50% | Needs the largest sample (most variance) |
| Small population | Apply the finite population correction |
Formula & methodology
Formula: n = z^2 x p(1-p) / e^2; then correct for finite population: n_adj = n / (1 + (n-1)/N)
The calculator finds the minimum number of responses needed for results within your chosen margin of error at a given confidence level. It uses the standard formula with p = 0.5 (the most conservative, highest-variance assumption) unless you supply an expected proportion. For small or known populations it applies the finite population correction so you don't over-sample. Tighter margins and higher confidence both demand larger samples.
Frequently asked questions
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