Sample Size Calculator
Calculate sample size using explicit client-side inputs.
Sample Size Calculator Inputs
Results computed instantly — your data never leaves your device.
Live Sample Size Calculator Results
Real-TimeRequired sample size
385
Rounded up from the proportion and margin assumptions.
How to Use the Sample Size Calculator
- 1
Enter the confidence z-score.
- 2
Enter the expected population proportion as a percent.
- 3
Enter the desired margin of error as a percent.
- 4
Review the rounded-up sample-size estimate.
Formula & Mathematical Basis
Variable Key
zCritical z-score for the chosen confidence level
pExpected population proportion as a decimal
eMargin of error as a decimal
📝 The interface accepts p and e as percentages and converts them to decimals before applying the formula; a zero margin returns a guarded zero.
Step-by-Step Examples
95% confidence planning estimate
Scenario: Use z = 1.96, p = 50%, and a 5% margin of error.
- 1.Convert 50% to p = 0.50 and 5% to e = 0.05.
- 2.Square the z-score: 1.96² = 3.8416.
- 3.Apply n = 3.8416 × 0.50 × 0.50 ÷ 0.05².
- 4.Round up to obtain 385 observations.
Practical Use Cases
- Plan a basic proportion survey.
- Explain how confidence and precision affect sample size.
- Compare sample requirements under different assumptions.
Common Pitfalls
- Entering 0.05 when the field already expects 5%.
- Using a z-score that does not match the confidence level.
- Treating the estimate as a substitute for a complex survey design.
Frequently Asked Questions
Why is the result rounded up?
A sample cannot contain a fraction of an observation, so the estimate is rounded upward.
Does this include finite-population correction?
No. The route uses the simple proportion estimate shown in its formula.
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