Margin of Error Calculator
Estimate a normal-approximation margin of error for a sample proportion from sample size, assumed proportion and critical z value.
How to use this calculator
- Enter sample size, expected or observed proportion percentage, and a critical z value suitable for your confidence level.
- Review the worked example for margin of error calculator and compare the inputs with your own units.
- Change one assumption at a time and recalculate if you need a second scenario.
Approximate proportion margin
Margin = z × square root[p(1 − p) ÷ n], where p is expressed between 0 and 1.
- This simple formula is a normal approximation under a simple random-sampling model and assumes observations are independent.
- The result is calculated from the values entered; the page does not independently verify assumptions, data quality or real-world suitability.
Worked examples
Approximate 95% survey margin
At n = 400, p = 0.50 and z = 1.96, the standard error is sqrt(0.25/400) = 0.025.
1.96 × 0.025 = 0.049, or 4.9 percentage points.
The approximate margin of error is ±4.9 percentage points.
Understanding the result
At a fixed sample size the margin is largest around a 50% proportion under this formula.
Sampling bias, nonresponse, clustering, weighting, finite populations and small samples can make this approximation unsuitable.
Important notes
Choose z for the confidence level and check the survey design rather than treating the margin as a full quality measure.
Displayed figures are rounded for readability. Preserve more precision during intermediate calculations and verify the labels and units before using the estimate.
Frequently asked questions
What does the Margin of Error Calculator show?
At a fixed sample size the margin is largest around a 50% proportion under this formula.
What assumptions should I check?
Choose z for the confidence level and check the survey design rather than treating the margin as a full quality measure.
Does this replace expert or authoritative guidance?
Sampling bias, nonresponse, clustering, weighting, finite populations and small samples can make this approximation unsuitable.
Related calculators
- Percent Error Calculator — Calculate percentage error and absolute error between observed and reference values.
- Proportion Calculator — Solve a simple proportion with three known values.
- Standard Error Calculator — Estimate the standard error of a sample mean from sample standard deviation and sample size.
- Circle Calculator — Calculate circle area, circumference, and diameter from radius.
- Pythagorean Theorem Calculator — Find the hypotenuse of a right triangle from the two perpendicular sides.
- Sample Size Calculator — Estimate a simple random-sample size for a proportion using a chosen confidence z-score, assumed proportion and margin of error.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- How to Calculate Salary from an Hourly Rate — Convert hourly pay into weekly, monthly, and annual estimates and understand the assumptions behind the result.
- Percent Difference — Understand percent difference, when it is appropriate, and how it differs from percentage change and percent error.
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.