Sample size calculator
Estimate the minimum sample size for a target confidence level and margin of error.
What this calculator covers
Use this calculator to turn confidence, margin of error, and an assumed proportion into a minimum response target.
It is useful for survey planning and quick estimation because it shows both the large-population baseline and the finite-population correction when you have a known population cap.
Frequently asked questions
- Why does a higher confidence level require a larger sample?
- A higher confidence level corresponds to a wider z-score, which appears as z² in the numerator of the sample-size formula. That larger multiplier drives the required count upward to maintain the stated certainty about where the true value falls.
- What should I enter for the population proportion if I have no prior estimate?
- Use 0.5. That value maximizes the product p × (1 − p) and therefore produces the most conservative, largest-possible sample size, which protects against underestimating what you need.
- When does the finite-population correction actually matter?
- The correction meaningfully reduces the required count only when your sample would be a substantial fraction of the total population — roughly when the uncorrected baseline exceeds 5–10% of the population size. For very large populations the correction has almost no effect.
- What does margin of error mean in this context?
- Margin of error is the maximum acceptable distance between the survey result and the true population value, expressed as a percentage. Cutting the margin of error in half roughly quadruples the required sample because the formula divides by e².
Tool
Run the calculation
Result
RESULT · MINIMUM SAMPLE SIZE
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Primary result
385 responses
At 95% confidence with a 5% margin of error and an assumed proportion of 50%, the minimum sample size is 385.
- Confidence z-score
- 1.959964
- Margin of error (decimal)
- 0.05
- Baseline sample size nâ‚€
- 384.1459
- Working sample size
- 384.1459
- Minimum whole-number sample
- 385
Step-by-step solution
- 1.Convert the design targets into z = 1.959964, margin of error e = 0.05, and p = 0.5.
- 2.Compute the infinite-population baseline n₀ = z² × p × (1 - p) / e² = 384.1459.
- 3.No finite population was supplied, so the uncorrected baseline is used as the working sample size.
- 4.Round up to the next whole response count: 385.
Walkthrough
Visual walkthrough
Sample-size planning turns confidence, margin of error, and an assumed proportion into a minimum response count.
01
Set the design targets
95% confidence · 5% margin · p = 0.5
Confidence determines the z-score, the margin of error sets the tolerated width, and p controls the expected spread.
02
Solve the baseline formula
nâ‚€ = 384.1459
The standard proportion formula gives the sample size needed when the population is effectively large.
03
Round to a usable target
Without a population cap, the baseline formula is simply rounded up to the next whole response count.
385 responses