What Is a Confidence Interval Calculator?
A confidence interval gives a range that likely contains the true population mean, based on your sample statistics and chosen confidence level. This calculator computes that range using the standard normal (z-score) method for large samples.
How to Use the Confidence Interval Calculator
- Enter your sample mean and standard deviation.
- Enter your sample size.
- Choose a confidence level (90%, 95%, or 99%).
Confidence Interval Formula
Worked Example
Standard error: 15 / √50 ≈ 2.121
Margin of error: 1.96 × 2.121 ≈ 4.16
95% CI: 100 ± 4.16 = 95.84 to 104.16
Understanding Your Results
A 95% confidence interval means that if you repeated this sampling process many times, about 95% of the calculated intervals would contain the true population mean. It does not mean there's a 95% probability the true mean falls in this specific interval — a common misinterpretation.
Common Mistakes to Avoid
- Misinterpreting confidence level as the probability the true mean falls in this specific interval.
- Using the z-score method with very small sample sizes, where a t-distribution is more appropriate.
Frequently Asked Questions
It means that if the sampling process were repeated many times, approximately 95% of the resulting intervals would contain the true population mean — not that there's a 95% chance this specific interval contains it.
Take the sample mean, then add and subtract the margin of error (z-score times standard error) to get the interval's upper and lower bounds.
1.645 for 90% confidence, 1.96 for 95% confidence, and 2.576 for 99% confidence are the standard values for two-tailed intervals.
Yes — larger sample sizes reduce standard error (since you divide by √n), producing a narrower, more precise confidence interval for the same confidence level.
Z-scores are appropriate for large samples (generally n ≥ 30) with known or well-estimated standard deviation; for smaller samples, a t-distribution is more statistically appropriate.