Sample Size Calculator
Survey & Study Planning Tool
For estimating a percentage or share of a population.
For estimating a numeric mean when the population standard deviation is known or estimated.
Understanding Sample Size
Sampling too few people risks unreliable results; sampling too many wastes time and money. Sample size calculation finds the smallest group that still gives you your desired precision and confidence.
Used for yes/no, pass/fail, or share-of-population questions — like an election poll or a product defect rate. The required sample size depends on your margin of error and how close to 50/50 the true split is expected to be.
Used when estimating a numeric average, such as average height or average purchase amount. The required sample size scales with the square of the population standard deviation and inversely with the square of your margin of error.
The Formulas
Proportion
Mean (Standard Deviation)
Finite population correction: nadj = n ÷ (1 + (n − 1) ÷ N), where N is the total population size.
Choosing Your Inputs
The margin of error is how much sampling error you're willing to tolerate — a tighter margin (e.g. ±2% instead of ±5%) requires a larger sample. The confidence level is how sure you want to be that your interval captures the true value; 95% is the most common standard. When you don't know the true proportion or standard deviation ahead of time, using a conservative estimate (0.5 for proportions) protects you from under-sampling.
Maximizes required sample size, so it's safe when the true proportion is unknown.
The most widely used confidence level for surveys and studies.
Shrinks the required sample when your population itself is small and known.
Key Takeaways
- Precision costs sample size. Halving your margin of error roughly quadruples the required sample.
- Use 0.5 for an unknown proportion to guarantee your sample is large enough regardless of the true split.
- Finite population correction only matters for small populations — its effect is negligible once N is much larger than n.
- Already have your data? Use the Confidence Interval Calculator to build an interval around your sample results.
Frequently Asked Questions
- Pick the Proportion tab if you're estimating a percentage/share (e.g. "what % of voters support X"), or the Standard Deviation tab if you're estimating a numeric mean and know (or can estimate) the population standard deviation.
- Choose a confidence level — 90%, 95%, or 99%.
- Enter your desired margin of error and the proportion or standard deviation for that tab.
- Optionally check "Apply finite population correction" and enter your total population size if it's known and relatively small.
- Click "Calculate" to see the required sample size.
The term p(1-p) in the sample size formula is largest when p = 0.5, which produces the largest — and therefore safest — required sample size. If you have no prior estimate of the true proportion, using 0.5 guarantees your sample is large enough no matter what the real proportion turns out to be.
The standard sample size formula assumes an effectively infinite population. When you're sampling a large share of a known, relatively small population (for example, surveying 200 people out of a town of 900), the finite population correction reduces the required sample size, since sampling a larger fraction of a small population gives you proportionally more information. It has little effect when the population is very large relative to the sample.
Use Proportion mode when your outcome is a percentage or a yes/no share of a population (e.g. approval ratings, defect rates). Use Standard Deviation mode when you're estimating a numeric average (e.g. average height, average spending) and you have an estimate of how spread out that data is.
Sample size must be a whole number of people or items, and rounding down would leave you slightly under-powered for your target margin of error and confidence level. The calculator always rounds the raw formula result up to the next whole number to guarantee the stated precision is met.
They're the standard critical values from the normal distribution for the most common confidence levels: 1.645 for 90%, 1.96 for 95%, and 2.576 for 99%. The same values are used by the Confidence Interval Calculator.