Sample Size Calculator
How many responses you needRuns locally · nothing uploaded
Required sample size
385
Sample size (infinite population)
385
z-score
1.96
How it works
When to use it
- Decide how many completed responses a survey needs.
- Justify sample size in a research proposal.
Formula
n₀ = z² × p × (1 − p) ÷ e²z = critical value (1.96 for 95%), p = expected proportion, e = margin of error.
Finite population: n = n₀ ÷ [1 + (n₀ − 1) ÷ N]Rounded up.
Worked example
Given: 95% confidence, ±5% margin, p = 50%, population 10,000
- n₀ = 1.96² × 0.25 ÷ 0.0025 ≈ 384.1 → 385.
- Corrected: 384.1 ÷ (1 + 383.1 ÷ 10,000) ≈ 369.9 → 370.
Result: At least 370 completed responses (385 for a very large population).
Reading the result
- Use p = 50% when unsure; it gives the largest, safest sample.
- Tightening the margin from 5% to 3% raises n from 385 to 1,068.
- Divide by the expected response rate to get how many people to invite.
Limitations
- For estimating one proportion under simple random sampling. Clustered designs need a design effect; comparing groups needs a power analysis.
- A biased sample stays biased no matter how large.
Sources
- Cochran WG. Sampling Techniques, 3rd ed. Wiley, 1977.
How to use
- 1Choose the confidence level (usually 95%).
- 2Enter the margin of error and expected proportion (50% if unsure).
- 3Optionally enter the population size.
FAQ
What formula is used?
n₀ = z²·p(1−p)/e², with the finite population correction n = n₀ / (1 + (n₀−1)/N).
Why use 50% as the proportion?
It maximizes p(1−p), giving the most conservative sample size when you have no prior estimate.