Margin of Error Calculator Formula
Understand the math behind the margin of error calculator. Each variable explained with a worked example.
Formulas Used
Margin of Error
moe = z * sigma / sqrt(n)Standard Error
se = sigma / sqrt(n)Relative Margin (%)
moe_pct = (z * sigma / sqrt(n)) * 100 / (sigma * sqrt(n) / sqrt(n))Variables
| Variable | Description | Default |
|---|---|---|
z | Z-Value | 1.96 |
sigma | Standard Deviation | 12 |
n | Sample Size | 100 |
How It Works
How to Calculate Margin of Error
Formula
E = z * (sigma / sqrt(n))
The margin of error is the half-width of the confidence interval. It depends on three factors: the confidence level (via z), the variability of the data (sigma), and the sample size (n). A smaller margin of error means a more precise estimate.
Worked Example
z = 1.96, SD = 12, n = 100. What is the margin of error?
z = 1.96sigma = 12n = 100
- 01Standard Error = 12 / sqrt(100) = 12 / 10 = 1.2
- 02Margin of Error = 1.96 * 1.2 = 2.352
- 03The sample mean will be within +/- 2.352 of the population mean with 95% confidence.
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