Margin of Error Calculator
Find the margin of error of a survey result or a sample mean at a chosen confidence level.
Margin of error (±)
3.099%
- Interval
- 46.901% to 53.099%
- Critical z
- 1.959963985
Show the work
Critical z for 95% confidence (two-sided)
z with 2.5% of the curve above it = 1.959963985
Standard error of the proportion
SE = √(p̂ × (1 − p̂) ÷ n)
√(0.5 × (1 − 0.5) ÷ 1,000) = 0.0158113883
Margin of error, as a percentage
E = z × SE × 100
1.959963985 × 0.0158113883 × 100 = 3.099%
How it works
Proportion: E = z √(p̂(1 − p̂) ÷ n); mean: E = z σ ÷ √n; with a finite population multiply by √((N − n) ÷ (N − 1))
Questions
- How does the margin of error calculator work?
- Proportion: E = z √(p̂(1 − p̂) ÷ n); mean: E = z σ ÷ √n; with a finite population multiply by √((N − n) ÷ (N − 1)).
- What do I need to enter?
- For a, Sample size (n), Confidence level, Sample proportion, Standard deviation (σ), Population size. Optional fields can be left blank.
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