Sample Size Calculator
Enter your desired margin of error, confidence level, and expected proportion to find the minimum sample size needed for your survey — with finite population adjustment and sample size vs. precision trade-off guidance.
Enter your values above to see the results.
Tips & Notes
- ✓Always use p=0.50 (50%) when you do not know the expected proportion. This gives the maximum (most conservative) sample size — any actual proportion will require fewer respondents.
- ✓Round sample size up, never down. If the formula gives n=1,067.4, collect n=1,068. Rounding down makes your actual margin of error slightly larger than your target.
- ✓Add a nonresponse buffer. If you need 400 completed surveys and expect 25% nonresponse, send invitations to 534 people. Plan for nonresponse before fieldwork, not after.
- ✓For comparing two proportions or two means, you need this calculated n in each group — multiply by 2 for the total sample. Two-group comparisons require more total respondents than single-proportion estimates.
- ✓Finite population correction can significantly reduce required sample size when N is small. Surveying 10,000 people from a population of 20,000 (50%) requires far fewer than 10,000.
Common Mistakes
- ✗Entering margin of error as a percentage (5) instead of a decimal (0.05). The formula uses ME as a decimal — entering 5 gives a sample size of 1, not 1,068. Always convert: 3% → 0.03, 5% → 0.05.
- ✗Forgetting to account for nonresponse. If you need 400 completed responses and expect 20% nonresponse, you must contact 500 people. Calculating only the required completed n without adding nonresponse leads to an undersized final sample.
- ✗Using the survey sample size formula for comparing means. The n=z*²p(1−p)/ME² formula applies to proportions. Comparing group means requires a different power analysis based on expected effect size and standard deviation.
- ✗Assuming calculated sample size guarantees the stated precision. The formula assumes a random probability sample. Convenience samples, self-selected respondents, or poorly defined sampling frames can produce biased results regardless of sample size.
- ✗Ignoring subgroup analysis needs. If you plan to analyze results separately for subgroups (by age, region, gender), each subgroup needs sufficient n. A total n=1,000 split into 5 regions gives only 200 per region — with much larger ME per region.
Sample Size Calculator Overview
Sample size calculation answers the most practical question in research planning: how many people do I need to survey? Too few respondents produce unreliable estimates with wide margins of error. Too many wastes resources. The right sample size gives you the precision you need at the confidence level you require — calculated before data collection, not after.
Sample size formula for a proportion:
n = z*² × p(1−p) / ME²
EX: ME=±3%, 95% confidence, p=0.50 → n = (1.96)² × (0.5×0.5) / (0.03)² = 3.8416 × 0.25 / 0.0009 = 0.9604/0.0009 = 1068 → round up to n=1,068Sample size with finite population correction:
n_adjusted = n / [1 + (n−1)/N]
EX: n=1,068, population N=5,000 → n_adjusted = 1068 / [1+(1067/5000)] = 1068/1.2134 = 880 → surveying 880 of 5,000 is sufficientCritical z-values by confidence level:
| Confidence Level | Z* | n for ME=±5% | n for ME=±3% | n for ME=±1% |
|---|---|---|---|---|
| 90% | 1.645 | 271 | 752 | 6,765 |
| 95% | 1.960 | 384 | 1,068 | 9,604 |
| 99% | 2.576 | 664 | 1,844 | 16,590 |
Frequently Asked Questions
Use the formula n = z*² × p(1−p) / ME². For 95% confidence (z*=1.96), unknown proportion (p=0.5), and ±3% ME: n = (1.96)² × 0.25 / (0.03)² = 3.8416 × 0.25 / 0.0009 = 1,068. Always round up. This is the minimum for completed responses — add a nonresponse buffer when planning fieldwork.
The sample size formula is maximized when p=0.5 — it produces the largest required n. Any other proportion (say p=0.2 or p=0.8) gives a smaller required sample. Using p=0.5 when the true proportion is unknown guarantees you will have sufficient sample size regardless of the actual result. This conservative approach avoids collecting too few respondents if the proportion turns out to be near 50%.
Sample size scales with 1/ME². Halving the margin of error from ±4% to ±2% quadruples the required sample: n at ±4% ≈ 600; n at ±2% ≈ 2,400. Tightening precision from ±3% to ±1% requires 9× the sample (1,068 vs. 9,604). This is why very precise surveys are expensive — small improvements in precision demand large increases in sample size.
When your sample represents more than 5% of the total population, the standard formula overestimates required sample size. The correction: n_adjusted = n / [1+(n−1)/N]. Example: standard formula gives n=1,068 for a population of N=3,000. Adjusted: 1068/(1+1067/3000) = 1068/1.356 = 788. You only need 788 instead of 1,068 — a 26% reduction. Apply this when N is known and n/N > 5%.
Surprisingly, for large populations, population size barely matters. The difference in required sample size between a population of 1 million and 10 billion is negligible (both require approximately 1,068 for ±3%, 95% CI). Population size only matters when you are sampling a substantial fraction of a small population — roughly when n/N > 5%. This is why a national poll of 1,000 is as statistically valid as a poll of 1,000 from a city.
The calculated n applies to the overall sample. For each subgroup you plan to analyze separately, that subgroup needs sufficient n on its own. If you need ±5% ME for each of 4 regions: n=384 per region, total n=1,536. If you calculate total n=1,000 and expect even splits: 250 per region with ME=±6.2% — which may be inadequate. Always identify analysis subgroups before calculating sample size and plan for the smallest subgroup's precision requirements.