Sample Size Calculator
Calculate the required sample size for surveys and statistical studies. Determine how many responses you need for statistically reliable results.
Sample Size Calculator
Calculate the required sample size for surveys and statistical studies
Higher confidence requires larger sample sizes
Smaller margin of error requires larger sample sizes
Use 50% if unknown (gives maximum sample size)
Formula
n = (Z² × p × (1-p)) / E²Where Z = Z-score for confidence level, p = expected proportion, E = margin of error. For finite populations, apply correction: n_adj = n / (1 + (n-1)/N)
Sample Size Guidelines
| Population Size | ±3% Error | ±5% Error | ±10% Error |
|---|---|---|---|
| 100 | 92 | 80 | 49 |
| 500 | 341 | 217 | 81 |
| 1,000 | 516 | 278 | 88 |
| 10,000 | 964 | 370 | 95 |
| 100,000+ | 1,067 | 383 | 96 |
* Based on 95% confidence level and 50% expected proportion
How to Use
- 1Select confidence level — Choose your desired confidence level (90%, 95%, or 99%).
- 2Set margin of error — Select the acceptable margin of error for your survey results.
- 3Enter expected proportion — Estimate the expected response proportion (use 50% if unknown).
- 4Add population size — Optionally enter your total population size for finite population correction.
- 5View results — See the required sample size for your survey.
Frequently Asked Questions
What is sample size?
Sample size is the number of observations or responses needed in a survey or study to achieve statistically reliable results. A larger sample size generally provides more accurate estimates.
What is margin of error?
Margin of error indicates the range within which the true population value is likely to fall. A ±5% margin of error means your results could be 5 percentage points higher or lower than the true value.
What confidence level should I use?
95% is the most commonly used confidence level in research. Use 99% for critical decisions requiring higher certainty, or 90% when resources are limited and some uncertainty is acceptable.
Why does population size matter?
For small populations, you can survey a smaller percentage and still get reliable results. The finite population correction reduces the required sample size when your population is known and limited.
What if I don't know the expected proportion?
Use 50% as the expected proportion. This gives the maximum (most conservative) sample size, ensuring your results will be reliable regardless of the actual proportion.