justyourcalculatorSample Size Calculator
Work out how many people to survey, or how precise your survey is.
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Sample Size Calculator
How many responses a survey needs
Use 50% if unsure (gives the largest, safest sample).
Leave empty for a very large or unknown population.
Sample size needed
385
for ±5% at 95% confidence
- Unrounded sample size
- 384.1459
- Z-score
- 1.959964
- Sample size for an unlimited population
- 385
How it was calculated
- z for 95% confidence = 1.959964
- n₀ = z² × p(1 - p) / E²
- n₀ = 1.959964² × 0.5 × 0.5 / 0.05² = 384.145882
- Round up: n = 385
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How the sample size calculator works
The sample size tells you how many responses you need so that your survey result is within a chosen margin of error of the true value, at a chosen confidence level. The formula is n = z² × p(1 - p) / E², where z comes from the confidence level (1.96 for 95%), p is the expected proportion and E is the margin of error.
If you don't know the proportion, use 50%: it gives the largest sample and so the safest answer. For a small population of known size N, the finite population correction n / (1 + (n - 1) / N) reduces the sample you need.
The margin of error tab reverses the formula: E = z × √(p(1 - p) / n). These formulas assume a simple random sample; real surveys with low response rates or clustered samples need more.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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