Confidence Interval Calculator
Build a confidence interval for a mean or a proportion.
What the Confidence Interval Calculator does
A confidence interval gives a range of plausible values for a population parameter, based on your sample. A 95% interval does not mean a 95% chance the true value is inside — it means 95% of intervals built this way would capture it.
Formula
Mean: CI = x̄ ± t × (s ÷ √n)Proportion: CI = p ± z × √(p(1−p) ÷ n)Finite population correction = √((N − n) ÷ (N − 1))
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Interval for | one of 2 options | Yes | — |
| Sample mean | number | In some modes | Shown Interval for is A mean. |
| Standard deviation | number | In some modes | Accepts more than 0. Shown Interval for is A mean. |
| Sample proportion | % | In some modes | Shown Interval for is A proportion. |
| Sample size (n) | number | Yes | Accepts 2 or more. |
| Confidence level | one of 6 options | Yes | — |
| Population size | number | Optional | Optional — applies a finite population correction. Accepts 0 or more. |
How to use it
- Choose Interval for and Confidence level.
- Enter Sample size (n).
- Fill in the remaining inputs the form shows for your choice.
- Optionally add Population size.
- Select Calculate.
Worked example
A sample of 50 with a mean of 72.4 and a standard deviation of 8.6, at 95% confidence.
- Mean
- 72.4
- SD
- 8.6
- Sample size
- 50
- Confidence
- 95%
SE = 1.216, t = 2.010, giving 69.96 to 74.84.
Frequently asked questions
What does 95% confidence actually mean?
That the procedure captures the true parameter 95% of the time across repeated sampling. Any single interval either contains it or does not — the probability describes the method, not the specific interval.
Should I use t or z?
t when the population standard deviation is unknown, which is nearly always. The two converge above about 30 observations.