Confidence Interval Calculator

A confidence interval is a range of values that, with a specified level of confidence (e.g. 95%), contains the true population parameter. CI = mean ± (z × standard error), where standard error = standard deviation ÷ √n.

95% confidence interval = mean ± 1.96 × (standard deviation ÷ √n). Example: mean=50, SD=10, n=100 → CI = 50 ± 1.96 × 1 = [48.04, 51.96].

Key Features

• Supports 90%, 95%, and 99% confidence levels.
• Calculates margin of error, lower bound, and upper bound.
• Works with any sample size (uses z-score for large samples).
• Runs entirely in your browser — no data sent anywhere.

How to Use the Tool

1. Enter the sample mean (average value).
2. Enter the standard deviation of the sample.
3. Enter the sample size (number of observations).
4. Select the confidence level (typically 95%).
5. The confidence interval bounds and margin of error display instantly.

Core Benefits

• Critical for research reports, academic papers, and A/B test analysis.
• Understand whether two measurements are statistically different.
• Avoids manual z-score lookup and formula errors.

Common Use Cases

• Reporting survey results with a stated margin of error.
• Analyzing A/B test results to determine statistical significance.
• Academic research: reporting the confidence interval for an experimental mean.
• Quality control: checking if a manufacturing process mean is within spec.

Pro Tips

• 95% CI uses z = 1.96. 99% CI uses z = 2.576. 90% CI uses z = 1.645.
• A wider CI means less precision (smaller sample or higher variability). Increase sample size to narrow it.
• Confidence level ≠ probability the interval contains the true value FOR THAT SPECIFIC INTERVAL. It means 95% of intervals from repeated samples would contain the true value.