What is Confidence Interval?
The Confidence Interval Calculator computes the range within which the true population mean is likely to fall, based on sample data. A 95% confidence interval means: if you repeated this sampling 100 times, about 95 of those intervals would contain the true population mean.
Confidence intervals are fundamental to statistics, used in scientific research, polling, clinical trials, quality control, and business analytics. They quantify the uncertainty in your estimate — a wider interval means less precision, a narrower interval means more precision.
The width of a confidence interval depends on three factors: (1) standard deviation (more variation = wider CI), (2) sample size (larger sample = narrower CI), and (3) confidence level (higher confidence = wider CI).
Formula
Confidence Interval = Mean ± z × (σ / √n)
Where: - z = z-score for confidence level 90% → z = 1.645 95% → z = 1.960 99% → z = 2.576 - σ = standard deviation - n = sample size - σ/√n = standard error (SE)
Example — Mean=50, SD=10, n=30, 95%: SE = 10/√30 = 1.826 MOE = 1.960 × 1.826 = 3.579 CI = [50 − 3.58, 50 + 3.58] = [46.42, 53.58]
We are 95% confident the true mean is between 46.42 and 53.58.
How to use this Confidence Interval Calculator?
1. Enter sample mean (average of your data). 2. Enter standard deviation (measure of spread). 3. Enter sample size. 4. Choose confidence level (95% is most common). 5. See the confidence interval bounds and margin of error.