Sample Size Calculator for Surveys (Proportion) and Means
Choose a proportion (survey percentage) or a mean, set the confidence level and margin of error, and optionally the population size. You get the minimum sample size, rounded up.
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Sample size needed
385
- Before rounding up
- 384.1459
- z for this confidence
- 1.96
Assumes a simple random sample. Add extra to allow for people who do not respond.
Show working
- z = Φ⁻¹(1 − α/2) = 1.96
- n₀ = z²·p(1 − p) / e² = 1.96² × 0.5 × 0.5 / 0.05² = 384.1459
- n = ⌈384.1459⌉ = 385
How to use
- Choose proportion (yes/no style surveys) or mean (measurements).
- Set the confidence level and margin of error (and the expected % or SD).
- Optionally enter the total population size, then read the sample size.
Good to know
Proportion: n₀ = z²·p(1 − p)/e². With 95% confidence (z = 1.96), ±5% margin and p = 50% (the safest guess), n₀ = 384.15, so you need 385 responses.
Finite population correction: n = n₀/(1 + (n₀ − 1)/N). For a population of 1,000 the 385 above drops to 278. For populations over about 1 lakh the correction hardly matters.
Mean: n = (z·σ/E)², where σ is the expected standard deviation (from a pilot study or past data) and E the margin of error in the same units. These are minimums for simple random samples; plan extra for non-response.
Questions
How many people do I need to survey for ±5% at 95% confidence?
About 385 for a large population, assuming p = 50%.
Why use p = 50%?
It gives the largest sample size, so it is safe when you have no idea of the true percentage.
Does a larger population need a much larger sample?
No. Above a few thousand people the required sample barely changes; 1 crore people still need about 385 for ±5%.
What about people who do not respond?
Divide by the expected response rate. If only 40% reply, invite about 385 ÷ 0.4 ≈ 963 people.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.