Sample Size Calculator
Calculate required sample size
Results
| Z-Score | — |
|---|---|
| Population Proportion (p) | — |
| Margin of Error (E) | — |
| Required Sample Size | — |
Under-powered surveys waste budget without reaching significance; over-powered ones burn time calling people you did not need. Before fieldwork starts, I like to lock sample size from confidence level, margin of error, and—when the audience is small—a finite population correction so the plan matches reality.
How to Use This Sample Size Calculator
- Set confidence level. Choose 90%, 95%, 99%, or a custom percentage. The tool converts this to a Z-score (about 1.96 at 95%).
- Enter margin of error. Typical values are 5%, 3%, or 1%—the maximum difference you accept between sample and population percentages.
- Optionally enter population size. Leave blank for a very large or unknown population. Enter N for a finite group (company roster, membership list) to apply correction.
- Set population proportion. Default 50% is the conservative maximum when you do not know the true yes/no split. Press Calculate—the required sample size rounds up to a whole number.
Sample Size Formulas and Practical Applications
Proportion surveys (support/oppose, defect rate, market share) share the same skeleton: square the Z-score, multiply by variability p(1 − p), divide by squared margin E, then adjust if the population is small.
Infinite or large population
n₀ = (Z² × p × (1 − p)) / E²
At 95% confidence (Z ≈ 1.96), p = 0.5, and E = 0.05, n₀ comes out near 385—the classic back-of-envelope figure for a ±5 point poll on a large population.
Finite population correction
n = (n₀ × N) / (n₀ + N − 1)
When N is only a few thousand, the corrected n drops below n₀ because you are sampling a sizable fraction of everyone. Skip N when the pool is city-sized or national—the correction barely moves the needle.
Choosing inputs in the field
- Marketing quick read: 95% confidence, 5% margin, p = 50% if unsure.
- Board-ready precision: 99% confidence, 3% margin—expect a much larger n.
- After fielding, build the interval around your result with the Confidence Interval Calculator.
Frequently Asked Questions
What is a Z-score in sample size calculation?
It is the normal critical value tied to your confidence level—higher confidence means a larger Z and a larger required n. The results table prints the Z used in your run.
Why does 50% population proportion give the largest sample size?
p(1 − p) maxes at 0.25 when p = 0.5. Any other split (30/70, 80/20) shrinks that product and lowers n₀, so 50% is the safe planning default.
When should I enter a finite population size?
Use N when sampling from a closed list—employees, association members, enrolled students. For open-ended populations, leave the field empty.
What margin of error should I use?
Match stakeholder tolerance: ±5% for directional insight, ±3% for standard media polls, ±1% when legal or safety decisions hinge on the percentage.
Does the result round up?
Yes—ceil ensures you never under-sample because of a fractional answer. For Z-score lookup on individual scores, see the Z-score Calculator or all math calculators.