Sample Size Calculator
Estimate an initial sample size for a proportion when you choose a confidence z-score, expected proportion and margin of error.
How to use this calculator
- Enter the values requested by the Sample Size and keep all units consistent.
- Check the formula and worked example before relying on the displayed result.
- Change one input at a time when comparing alternative scenarios.
Formula and method
n = z² × p(1 − p) ÷ E², where p and E are proportions
- The calculator applies the stated relationship to the inputs entered by the visitor. Intermediate calculations use full numeric precision before display rounding.
- Sampling design, nonresponse and a finite population may require adjustments.
Worked examples
Worked example: Sample Size
At z = 1.96, p = 0.5 and margin E = 0.05
n = 1.96² × 0.25 ÷ 0.05² ≈ 384.16, rounded up to 385.
n = 1.96² × 0.25 ÷ 0.05² ≈ 384.16, rounded up to 385.
Understanding the result
Use the output as a calculation for the chosen assumptions, not as an explanation of why a real-world result occurred.
Sampling design, nonresponse and a finite population may require adjustments.
Important notes
Sampling design, nonresponse and a finite population may require adjustments.
Confirm the units, source measurements, rounding convention and context before using the result for a real project or decision.
Frequently asked questions
What does this Sample Size calculate?
Estimate an initial sample size for a proportion when you choose a confidence z-score, expected proportion and margin of error.
Which assumptions matter most?
Sampling design, nonresponse and a finite population may require adjustments.
Can the result replace professional or domain-specific guidance?
No. The tool provides arithmetic under its stated assumptions; check applicable specifications, accounting conventions, standards or qualified guidance for consequential decisions.
Related calculators
- Proportion Calculator — Solve a simple proportion with three known values.
- Circle Calculator — Calculate circle area, circumference, and diameter from radius.
- Margin of Error Calculator — Estimate a simple proportion margin of error from sample size, assumed proportion, and a critical z value.
- Pythagorean Theorem Calculator — Find the hypotenuse of a right triangle from the two perpendicular sides.
- Standard Deviation Calculator — Calculate population or sample standard deviation, variance, mean, sum, and count.
- Standard Error Calculator — Estimate the standard error of a sample mean from sample standard deviation and sample size.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.