Free Sample Size Calculator
Calculate the minimum sample size for surveys, research studies, polls, and A/B tests. Enter your confidence level, margin of error, and population size. Free, private — all calculations run in your browser.
Sample Size Calculator — Survey, Study & Poll Design
Determine the minimum sample size needed for statistically valid surveys, polls, and clinical studies. Supports proportion-based and mean-based designs. Includes finite population correction and a reference table comparing margins of error at three confidence levels.
| Margin of Error | 90% CI | 95% CI | 99% CI |
|---|---|---|---|
| 1% | 6,766 | 9,604 | 16,590 |
| 2% | 1,692 | 2,401 | 4,148 |
| 3% | 752 | 1,068 | 1,844 |
| 5% | 271 | 385 | 664 |
| 10% | 68 | 97 | 166 |
How to Use This Calculator
- 1
Choose a study type: Proportion (yes/no questions) or Mean (continuous measurements).
- 2
Set the confidence level — 95% is the research standard.
- 3
Enter the margin of error — 5% for surveys, smaller for research.
- 4
For proportion studies: enter the expected proportion (0.5 = most conservative).
- 5
Enter the population size if known — leave blank for very large populations.
📐 How This Is Calculated
Proportion: n = Z²×p(1−p) / e² | Mean: n = Z²×σ² / e² | Finite: n_adj = n / (1+(n−1)/N)
Z—Critical z-value for chosen confidence level (e.g., 1.960 for 95%)p—Expected proportion (use 0.5 if unknown — maximizes sample size)e—Margin of error — maximum acceptable deviation from true valueσ—Population standard deviation (needed for mean-based studies)N—Total population size for finite population correctionReference: Cochran (1977) — Sampling Techniques; AAPOR Standard Definitions; FDA Guidance for Clinical Trials
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Disclaimer
Results are provided for informational and educational purposes only. They should not be used as a substitute for professional financial, engineering, medical, or legal advice. Always verify outputs with a qualified professional before making important decisions. Roughtools makes no warranties regarding accuracy or completeness for your specific situation.
About This Sample Size Calculator
Sample size is one of the most critical — and most commonly under-planned — aspects of research design. Too small a sample and your results are unreliable, potentially misleading decision-makers with false precision. Too large a sample and you waste resources, time, and money collecting more data than your analysis requires. This calculator tells you exactly how many responses, participants, or observations you need to achieve a specified level of statistical precision.
The Formula — How It Works
For surveys and proportion-based studies, the standard sample size formula is:
Where: z = z-score for confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p = expected population proportion (use 0.5 if unknown — this maximises and thus bounds the sample size), e = desired margin of error as a decimal (e.g., 0.05 for ±5%).
For finite populations (when your total population N is known and not very large), apply the finite population correction (FPC):
The FPC reduces the required sample when N is small relative to n. For N > 100,000, the correction is negligible (<0.4%) and the unadjusted formula suffices — this explains the well-known result that national polls need only ~1,000 respondents regardless of whether the population is 10 million or 300 million.
Confidence Levels, Margin of Error, and Population Proportion
The confidence level (90%, 95%, 99%) tells you how often your interval would capture the true population value if you repeated the study many times. 95% is the field standard — accepted by most academic journals, IRBs, and regulatory bodies. The margin of error (±e) is the acceptable range of imprecision around your estimate. ±5% is typical for general surveys; ±3% for higher-stakes research. The population proportion (p) is your best estimate of the true proportion you are measuring. When uncertain, p = 0.5 is the conservative choice because p(1−p) is maximised at p = 0.5, producing the largest (most conservative) sample size.
Why Sample Size Matters for Research Validity
An underpowered study is not just statistically inconvenient — it can be unethical. In clinical research, an underpowered trial exposes participants to risk without generating actionable evidence. In market research, decisions based on too-small samples lead to failed product launches. In public policy, poorly sampled surveys produce misleading pictures of public opinion. This calculator gives you the tools to plan research correctly from the start, before a single data point is collected.
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When to Use This Calculator
Determine how many respondents your customer satisfaction survey, employee pulse survey, or market research poll needs to produce statistically valid results.
Calculate how many visitors or sessions each variant of your A/B test needs before you can draw statistically significant conclusions about conversion rate differences.
Establish the minimum number of participants needed before beginning patient recruitment — a regulatory requirement for most clinical and epidemiological studies.
Scope the cost and timeline of primary market research by knowing exactly how large your survey panel needs to be to meet your precision requirements.
Determine the number of items to inspect in a manufacturing run or financial audit to achieve a given confidence level about the defect or error rate.
💡 Pro Tips
Halving your margin of error quadruples your required sample size — this is the inverse square law of sampling precision. Going from ±5% to ±2.5% does not double the sample; it multiplies it by four. Before demanding tighter margins, ask whether the precision gain is worth the cost. Often ±5% is more than sufficient for decision-making.
When the true population proportion is unknown, always use p = 0.5 (worst case) for your sample size calculation. This ensures your sample will be large enough whatever the true proportion turns out to be. If you use an assumed p = 0.3 and the true proportion is 0.5, your actual margin of error will be wider than planned.
Adjust for expected response rate. If you calculate you need 385 completed responses and you expect a 40% response rate, you need to recruit 385 / 0.40 = 963 initial invitations. This "gross sample" calculation is essential for survey planning — failing to account for non-response is a leading cause of underpowered studies.
Sub-groups need their own calculations. If you want to compare results between men and women, each group individually needs to meet your minimum sample size target. Plan sub-group quotas into your study design — you cannot fix an underpowered sub-group after data collection is complete.
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