👥 Sample Size Calculator
Estimate the required sample size for a population proportion using confidence level, margin of error, and expected proportion.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Estimate the required sample size for a population proportion using confidence level, margin of error, and expected proportion.
| Concept | Formula or rule |
|---|---|
| Sample Size Calculator | n₀ = z²p(1−p) / E² |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: At 95% confidence, 5% margin of error, and p=0.5, the large-population estimate is about 385.
✓ n ≈ 385
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Entering 5 as 0.05 in a percentage field
This field expects 5 for 5%.
This field expects 5 for 5%.
⚠️
Using an optimistic proportion without evidence
p=50% is conservative when unknown.
p=50% is conservative when unknown.
⚠️
Ignoring nonresponse
Recruit more participants than the minimum when response rates are below 100%.
Recruit more participants than the minimum when response rates are below 100%.
Practice Questions
1. Does halving margin of error roughly quarter or quadruple n?
Answer: Quadruple.
2. What p is safest when unknown?
Answer: 50%.
3. Does 99% confidence require more n than 95%?
Answer: Yes.
Frequently Asked Questions
Why does p=50% give the largest sample?▾
p(1−p) is maximized at 0.5.
What is finite population correction?▾
It reduces required n when sampling a substantial portion of a known finite population.
Does a larger confidence level require more data?▾
Yes.