Confidence Interval Calculator
Estimate the confidence interval for a population mean from your sample mean, standard deviation and size.
Confidence level
95% CI: 94.6323 to 105.3677
94.6323
105.3677
5.3677
2.7386
1.96
100
Formula
About this calculator
A confidence interval is a range of plausible values for a population parameter, calculated from a sample. A 95% confidence interval means that if you repeated the sampling process many times, about 95% of the intervals produced would contain the true population mean. The width of the interval reflects how much uncertainty there is in the estimate.
This calculator uses the z-based formula x̄ ± z × (σ / √n), where σ / √n is the standard error of the mean and z is the critical value for your chosen confidence level (1.645 for 90%, 1.96 for 95%, and 2.576 for 99%). Larger samples shrink the standard error and narrow the interval, while higher confidence levels widen it. The z-method assumes a known standard deviation and a reasonably large sample.
Frequently asked questions
It means that if you repeated your study many times, roughly 95% of the resulting intervals would capture the true population mean. It is not the probability that this particular interval contains the mean.
These are the critical z-scores from the standard normal distribution that leave 10%, 5% and 1% of the area in the two tails — corresponding to 90%, 95% and 99% confidence levels.
Increase your sample size, which reduces the standard error (σ / √n), or accept a lower confidence level. A larger sample is usually the most reliable way to tighten the interval.
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