📐 Confidence Interval Calculator
A sample average is never the whole story — the confidence interval is the range where the true average most likely hides. It equals your sample mean plus or minus a margin of error built from the spread of your data and how many samples you took.
Bigger samples shrink the interval (error falls with the square root of n), while higher confidence — say 99% instead of 95% — widens it, because claiming more certainty needs a bigger net.
How to use this calculator
Enter the sample mean, standard deviation, sample size and confidence level. The calculator returns the margin of error and the lower and upper bounds.
- Type the sample mean from your data.
- Type the standard deviation of your data.
- Type the sample size n.
- Pick the confidence level and press Calculate for the margin of error and interval.
Frequently asked questions
What does this confidence interval calculator compute?
It computes the margin of error as z times the standard deviation divided by the square root of n, then adds and subtracts it from the sample mean to give the interval where the true average most likely lies.
Can you show a worked example?
A mean of 100 with a standard deviation of 15 from 36 samples at 95 percent confidence gives a margin of error of 4.9, so the interval is 95.1 to 104.9.
Why does a bigger sample give a narrower interval?
The margin of error divides by the square root of the sample size, so quadrupling your sample roughly halves the error. Each extra response buys less precision than the last.
What does 95 percent confidence actually mean?
It means that if you repeated the whole sampling process many times, about 95 percent of the intervals you built would contain the true average. It does not mean there is a 95 percent chance this particular interval contains it.