Proportion Confidence Interval Calculator
Compute the confidence interval for a population proportion: p ± z·√[p(1−p)/n].
Input Data
Typically 95%.
Sample proportion in percent (0–100).
%
Sample size.
Results
—%
—%
At a glance:CI = p ± z·√[p(1−p)/n], with z = 1.96 at 95% confidence.
Formula
CI = p ± z√(p(1−p)/n)
$$p \pm z\sqrt{\frac{p(1-p)}{n}}$$How to Use
- Choose a confidence level (usually 95%).
- Enter the sample proportion p and sample size n.
- Read the lower and upper bounds of the confidence interval.
- Interpretation: the true population proportion falls in this interval with (confidence level)% probability.
FAQ
What if the sample proportion is near 0 or 100%?
The normal approximation may then be poor; use an exact method (Clopper–Pearson) or a log transformation. This calculator uses the normal approximation, so it is best when p is between 5%–95% and n is large enough.
What is the relationship between confidence interval and margin of error?
The half-width of the interval is exactly the margin of error MoE = z·√[p(1−p)/n], so CI = p ± MoE.
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.