Confidence Interval Calculator
Estimate the plausible range for a population mean given sample statistics and a desired confidence level.
Enter as decimal (e.g., 0.95 for 95% confidence).
Z-score
1.960
95.0% confidence
Standard Error
0.6938
s / √n
Margin of Error
1.3598
Z × SE
Confidence Interval
(23.2402, 25.9598)
x̄ ± 1.3598
How to Use This Calculator
- Enter the sample mean, standard deviation, and number of observations.
- Specify the desired confidence level between 60% and 99.9%.
- Review the resulting margin of error and interval bounds.
- Interpret the interval as the plausible range for the population mean.
Formula Reference
SE = s / √n
MOE = z × SE
CI = x̄ ± MOE
This calculator uses z-scores suitable for large samples or when the population standard deviation is known. For small samples with unknown σ, consider substituting a t-score with n − 1 degrees of freedom.
Frequently Asked Questions
When should I use a t-distribution?
Use t-scores when the population standard deviation is unknown and the sample size is small (typically n < 30).
Can I use this for proportions?
For proportions replace x̄ with p̂ (sample proportion) and use the standard error √[p̂(1 − p̂)/n].
How does the confidence level affect results?
Higher confidence levels increase the z-score and margin of error, producing wider intervals. Lower confidence narrows the interval but offers less assurance the population mean lies inside.