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Sample Size Calculator
Calculate the required sample size to estimate a proportion with your chosen margin of error and confidence level. Uses Cochran's formula with optional finite population correction.
Input Parameters
%
%
Apply finite population correction
Required Sample Size
385
respondents
Confidence
95%
Margin of Error
±5%
How We Calculate
Cochran's Formula (infinite population):
n₀ = (Z² × p × q) / e²Z = 1.96 (for 95% confidence)
p = 0.50 (expected proportion)
q = 0.50 (1 - p)
e = 0.05 (margin of error)
Results are rounded up to ensure the target margin of error is not exceeded.
Built by Lensym — focused on valid, reliable survey research.
Understanding Sample Size
Sample size determines the precision of your survey results. A larger sample reduces random error (measured as margin of error), but has diminishing returns beyond a certain point.
When to Use This Calculator
- Planning a survey and need to know how many responses to collect
- Determining if your existing sample is large enough
- Calculating sample size for academic research with specific precision requirements
Key Assumptions
- Simple random sampling — Each member of the population has an equal chance of selection
- Single proportion estimation — You're measuring a percentage (e.g., "60% prefer option A")
- Unknown variance handled conservatively — Using p = 0.5 produces the largest (most conservative) sample size when you don't know the true proportion
What This Calculator Does Not Account For
- Non-response bias — If non-respondents differ systematically from respondents
- Cluster or stratified sampling — More complex sampling designs require different formulas
- Multiple comparisons — Subgroup analysis requires larger samples per group
For a deeper discussion of sample size limitations, see our guide on why more responses doesn't always mean better data.