Margin of Error Calculator
Calculate the margin of error for a survey or poll given sample size and confidence level.
About Margin of Error Calculator
The margin of error tells you how far your survey results might be from the true population value. It depends on the sample size, the estimated proportion, and the desired confidence level.
Formula
MOE = z × √(p(1−p) / n)
- z
- Critical z-value for confidence level
- p
- Estimated proportion
- n
- Sample size
Worked example
With the default values below, Margin of Error Calculator returns Margin of Error of 4.38%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Sample Sizeminimum 1
- 500
- Proportion (0–1)accepts 0–1
- 0.5
- Confidence Level (%)accepts 50–99.99
- 95
Results
- Margin of Error
- 4.38%
- Z Critical Value
- 1.9600
- Lower Bound
- 45.62%
- Upper Bound
- 54.38%
Step by step
- 1Values used
- 2Formula applied
- 3Margin of Error= 4.38
- 4Z Critical Value= 1.9600
- 5Lower Bound= 45.62
- 6Upper Bound= 54.38
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why use p = 0.5?
p = 0.5 gives the maximum (most conservative) margin of error. If you don't know the true proportion, 0.5 is the safest assumption.
How do I reduce the margin of error?
Increase the sample size. Quadrupling the sample cuts the margin of error in half.