Mathematics

Sample Size Calculator

Confidence Level

Margin of Error (%)

Population Proportion (%)

Population Size (optional)

What is Sample Size Calculator?

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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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How to Sample Size Calculator

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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)

Worked Examples

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Example 1

Given:95% CI, ±5% margin, unknown proportion

Result:n = 385

The standard "385 rule" for large populations

Example 2

Given:99% CI, ±3% margin

Result:n = 1,844

Higher confidence and precision requires much larger sample

Sample Size Quick Reference (95% CI)

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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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Pro Tip

Always recruit slightly more than your target sample size to account for non-response and dropout. A 20% buffer is common in research.

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Did you know?

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

›Sample size determination — Wikipedia

Mathematically verified

Reviewed October 2026

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Sample Size Calculator