Find the margin of error and interval for a sample mean at your chosen confidence level.
How the confidence interval calculator works
A confidence interval gives a range that likely contains the true mean. Enter your sample mean, standard deviation and size, pick a confidence level, and this calculator returns the margin of error and the interval.
It uses the normal (z) approximation, which suits larger samples.
Step by step
- Enter the sample mean and standard deviation.
- Enter the sample size.
- Choose a confidence level and read the interval.
The maths behind it
margin = z × (standard deviation ÷ √n)
interval = mean ± margin
The default scenario, worked through
On the values this calculator opens with, the margin of error is ±5.368. Underneath, Lower bound comes out at 94.632 and Upper bound at 105.368. Change any field and every figure updates as you type.
Common questions
What is a confidence interval?
A range around your estimate that would contain the true value in, say, 95% of repeated samples.
What does 95% confidence mean?
If you repeated the study many times, about 95% of the intervals would contain the true mean.
Should I use z or t?
This tool uses z, which is fine for larger samples. Very small samples use the t-distribution instead.