Margin of Error Calculator
Compute the margin of error MoE = z·√[p(1−p)/n] for a proportion.
Input Data
Typically 95%.
Sample proportion in percent (0–100).
%
Sample size.
Results
3.099%
At a glance:MoE = z·√[p(1−p)/n], with z = 1.96 at 95% confidence.
Formula
MoE = z · √(p(1−p)/n)
$$MoE = z\sqrt{\frac{p(1-p)}{n}}$$How to Use
- Choose a confidence level (usually 95%).
- Enter the sample proportion p and sample size n.
- The calculator outputs the margin of error MoE (in percentage points).
- The result interval is estimate ± MoE.
FAQ
How does sample size affect the margin of error?
Margin of error is inversely proportional to √n. Quadrupling the sample size halves the MoE — that is why large surveys give narrower confidence intervals.
Why is ±3% so common?
At 95% confidence, p=50% and n≈1000, MoE ≈ 1.96·√(0.25/1000) ≈ 3.1%, which is exactly where the common poll claim of '±3%' comes from.
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.