Sample Size Calculator
Sample size is the number of observations needed to estimate a population parameter within a specified margin of error at a given confidence level. Larger samples give more precise estimates, but the relationship is not linear — quadrupling the sample only halves the margin of error.
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Tip: Always recruit slightly more than your target sample size to account for non-response and dropout. A 20% buffer is common in research.
- 1Determine your confidence level (usually 95%) and margin of error (usually ±5%)
- 2Estimate the proportion p (use 50% if unknown — gives the most conservative/largest sample)
- 3Formula: n = z²×p×(1−p) / e²
- 4For finite populations, apply correction: n_adjusted = n / (1 + (n−1)/N)
95% CI, ±5% margin, unknown proportion=n = 385The standard "385 rule" for large populations
99% CI, ±3% margin=n = 1,844Higher confidence and precision requires much larger sample
| Margin of Error | p=50% (worst case) | p=30% | p=10% |
|---|---|---|---|
| ±1% | 9,604 | 8,068 | 3,457 |
| ±2% | 2,401 | 2,017 | 864 |
| ±3% | 1,068 | 897 | 384 |
| ±5% | 385 | 323 | 138 |
| ±10% | 97 | 81 | 35 |
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Fun Fact
National polls of 1,000–1,500 people can represent a country of 300 million with only ±3% margin of error. The key is random selection — a biased sample of 1 million is worse than a random sample of 1,000.
References
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