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