Confidence Interval Calculator
Calculate confidence intervals for means and proportions with visual representation of the results.
Calculator Parameters
Confidence Interval
Visualization
Margin of Error
–
Standard Error
–
Formula & Explanation
Confidence Interval Formula
Where:
x̄ = Sample Mean
Z = Z-score (based on confidence level)
σ = Standard Deviation
n = Sample Size
Interpretation
A 95% confidence interval means that if we were to take 100 different samples and compute a confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true population mean.
Example: With 95% confidence, the population mean is between [lower bound] and [upper bound].
Practical Examples
Quality Control
A factory measures the length of 100 parts with mean 50mm and SD 2mm. The 95% CI for the true mean length is 49.61mm to 50.39mm.
Medical Research
A drug trial with 200 patients shows average systolic BP reduction of 8mmHg with SD 3mmHg. The 95% CI is 7.58mmHg to 8.42mmHg.
Education
Test scores from 500 students have mean 75 and SD 10. The 99% CI for the true mean score is 73.85 to 76.15.