This free Sample Size Calculator helps you determine how many participants, respondents, or observations you need to achieve reliable results in surveys, polls, and experiments. Enter your confidence level, margin of error, population size, and estimated proportion (or standard deviation) to instantly calculate the minimum required sample size.
Sample size is the number of participants or data points selected from a larger population. Choosing the right sample size ensures your results are statistically valid, representative, and precise enough for decision-making.
Too small a sample → unreliable, high error.
Too large a sample → waste of time and resources.
The calculator uses Cochran’s formula for proportions and the standard formula for means to give exact and rounded sample sizes.
$$ n_0 \;=\; \frac{Z^{2}\, p(1-p)}{E^{2}} $$
$$ n \;=\; \frac{n_0}{\,1 + \dfrac{n_0 - 1}{N}\,} $$
$$ n \;=\; \left(\frac{Z \,\sigma}{E}\right)^{2} $$
Choose whether you need sample size for a proportion (e.g., % of people who agree) or a mean (e.g., average score).
Select your confidence level (90%, 95%, 99% or custom).
Enter your margin of error (e.g., 5% → 0.05).
Provide an estimated proportion (p) or standard deviation (σ), depending on mode.
(Optional) Enter population size for finite correction.
Click Calculate to get:
Initial required sample size (n₀)
Adjusted sample size with finite correction (if applicable)
Final recommended sample size (rounded up)
Survey with population 10,000
$$ n_0 = \frac{1.96^2 \cdot 0.5(1-0.5)}{0.05^2} = 384.16 $$
$$ n = \frac{384.16}{1 + \dfrac{384.16 - 1}{10000}} \approx 370 $$
✅ Answer: A sample size of 370 respondents is required.
Q: What if I don’t know the proportion (p)?
A: Use 0.5 for the most conservative (largest) sample size.
Q: Why does population size matter?
A: For small populations, the finite correction reduces the required sample size.
Q: What confidence level should I use?
A: 95% is standard; 99% gives higher certainty but requires larger samples.
Q: Is a bigger sample size always better?
A: Not necessarily. Beyond a point, larger samples don’t significantly improve precision but increase cost.