Free confidence interval calculator: enter the sample mean, standard deviation and size to get the margin of error and 90%, 95% or 99% interval instantly.
A confidence interval turns a single sample mean into a range that probably contains the true population mean. For example, a sample mean of 100 with a margin of error of 4.16 gives a 95% interval from 95.84 to 104.16.
This confidence interval calculator computes the margin of error and the interval for the 90%, 95% and 99% confidence levels. Researchers, students and quality teams use it to report how precise an estimate is.
The calculator uses the standard normal distribution (z*), which is the standard approach for large samples — see the FAQ for when the t-distribution is more appropriate.
Enter the sample mean, the standard deviation and the sample size, then pick a confidence level; the margin of error, bounds and critical value update instantly.
If you repeated the sampling many times, about 95% of intervals built the same way would contain the true mean. It is not a 95% chance that the true mean is inside this particular interval.
CI = mean ± z* × σ / √n, with z* = 1.645 (90%), 1.96 (95%) or 2.576 (99%). Example: mean 100, σ 15, n 50 → 95% CI [95.84, 104.16].
The margin of error shrinks with √n: quadrupling the sample size halves the margin of error.
For small samples (n < 30) with an unknown population standard deviation, the t-distribution gives wider, more accurate intervals. This calculator uses the normal approximation common for n ≥ 30.
For a proportion p from n trials, the standard error is √(p(1−p)/n) and CI = p ± z* × SE. This calculator handles means; you can enter the proportion p as the mean to get a quick estimate.