Professional Confidence Interval Calculator

Calculate confidence intervals for population means and proportions. Supports z-interval and t-interval with step-by-step solutions.

Calculator

Enter your data to calculate the confidence interval for population mean or proportion.

Complete User Guide

What is a Confidence Interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a specified level of confidence. For example, a 95% confidence interval means we are 95% confident that the true population parameter lies within the calculated range.

Confidence intervals are used in statistics to estimate population parameters when we only have sample data.

How to Use This Calculator

  1. Select calculation type: Mean or Proportion
  2. Enter your sample data (mean/proportion, sample size, standard deviation for mean)
  3. Select or enter your desired confidence level (90%, 95%, 99%, or custom)
  4. For mean calculations, check if population standard deviation is known (z-interval) or unknown (t-interval)
  5. Click Calculate to get the confidence interval with step-by-step solution
  6. Review the results, visualizations, and detailed explanation

Understanding Your Results

Confidence Interval

The range of values that likely contains the true population parameter. For example, [45.2, 54.8] means we are confident the true value lies between 45.2 and 54.8.

Margin of Error

Half the width of the confidence interval. It represents the maximum amount by which the sample statistic may differ from the true population parameter.

Z-Interval vs T-Interval

Z-interval is used when population standard deviation is known. T-interval is used when only sample standard deviation is known, accounting for additional uncertainty.

Examples

Example 1: Mean Confidence Interval

Sample Mean: 50, Sample Size: 100, Standard Deviation: 10, Confidence Level: 95%

Result: 95% CI = [48.04, 51.96]

Interpretation: We are 95% confident the true population mean lies between 48.04 and 51.96.

Example 2: Proportion Confidence Interval

Sample Proportion: 0.45, Sample Size: 200, Confidence Level: 95%

Result: 95% CI = [0.381, 0.519]

Interpretation: We are 95% confident the true population proportion lies between 38.1% and 51.9%.

Important Notes

  • Sample size must be at least 2 for valid calculations.
  • For proportions, the value must be between 0 and 1.
  • Larger sample sizes result in narrower confidence intervals (more precise estimates).
  • Higher confidence levels result in wider intervals (less precise but more confident).

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