Sample Size Calculator
Find the minimum number of responses needed for a survey or experiment: n = z²·p(1−p)/e², adjusted for finite populations. Enter a confidence level, margin of error and expected proportion (50% if unsure).
TheCalculators — Sample Size Calculator
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Required sample size
385
95% confidence · ±5% margin · p = 50%
- Confidence level
- 95%
- z score
- 1.96
- Margin of error (e)
- 5%
- Proportion (p)
- 50%
- Unadjusted n₀ = z²p(1−p)/e²
- 384.15
- Adjusted n′
- — (not needed)
- Minimum sample size
- 385
Step-by-step solution
- 1Find z for the confidence levelz = normInv(1 − (1 − 95%)/2) = 1.96
- 2Apply the sample size formulan₀ = z²·p(1−p)/e² = 1.96² × 0.5×0.5 / 0.05² = 384.15
- 3Round upAlways round up: n = 385 respondents
p = 50% maximizes p(1−p), giving the largest (safest) required sample. If you expect roughly 80/20, entering the real proportion shrinks n.
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Formula
n = z²·p(1−p)/e² · finite population: n′ = n/(1 + (n−1)/N)
Pro tips
- • Use p = 50% when you have no prior estimate — it is the worst case.
- • Tightening the margin from 5% to 3% roughly triples the required sample.
- • Finite populations (classrooms, companies) need fewer samples thanks to the correction factor.
FAQ
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