Confidence Interval Calculator

Use this calculator to compute the confidence interval or margin of error, assuming the sample mean most likely follows a normal distribution

Use this calculator to compute the confidence interval or margin of error, assuming the sample mean most likely follows a normal distribution.

Input Values

%

About Confidence Intervals

A confidence interval provides a range of values that is likely to contain the true population parameter with a specified level of confidence.

Formula:

CI = X̄ ± Z × (s / √n)
• X̄ = sample mean
• Z = Z-score for confidence level
• s = sample standard deviation
• n = sample size

Common Z-scores:

  • 90%: Z = 1.645
  • 95%: Z = 1.960 (most common)
  • 98%: Z = 2.326
  • 99%: Z = 2.576

Interpretation:

  • 95% CI: We are 95% confident the true mean lies in this interval
  • Margin of Error: Half the width of the confidence interval
  • Larger sample: Smaller margin of error
  • Higher confidence: Wider interval

Applications:

  • • Survey research
  • • Medical studies
  • • Quality control
  • • Market research
  • • Scientific experiments
  • • Polling and elections