Calculate confidence intervals for population parameters based on sample data. This tool helps you estimate the range within which the true population mean is likely to fall, given your sample statistics and desired confidence level.
Results
Confidence Level:
Z-Score:
Standard Error:
Margin of Error:
Lower Bound:
Upper Bound:
Confidence Interval:
How to Use This Calculator
Enter Sample Mean: Input the average value from your sample data
Enter Standard Deviation: Provide the standard deviation of your sample or population
Enter Sample Size: Specify the number of observations in your sample (must be at least 2)
Select Confidence Level: Choose your desired confidence level (90%, 95%, or 99%)
Calculate: Click the button to compute your confidence interval
Understanding Confidence Intervals
A confidence interval provides a range of values that likely contains the true population parameter. For example, a 95% confidence interval means that if you were to repeat the sampling process 100 times, approximately 95 of those intervals would contain the true population mean.
Formula Used
The confidence interval is calculated using the formula:
CI = x̄ ± (Z × SE)
x̄ = Sample mean
Z = Z-score corresponding to the confidence level
SE = Standard Error = σ / √n
n = Sample size
Important Notes
This calculator assumes a normal distribution or large sample size (n ≥ 30)
For small samples from non-normal populations, consider using a t-distribution instead
The wider the confidence interval, the more uncertain the estimate
Larger sample sizes generally produce narrower, more precise confidence intervals