Confidence Interval Calculator
Find the confidence interval for a mean from the sample size, mean and standard deviation, at any confidence level.
Change the values and press Calculate to work out your own figures.
Enter the sample size, mean, standard deviation and confidence level.
Show the working
- z for 95% = 1.959963985
- margin = z × σ ÷ √n = 1.959963985 × 3.2 ÷ √50 = 0.8869784476
How to use it
Enter the sample size, mean, standard deviation and confidence level.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
CI = x̄ ± z × σ ÷ √n
What the interval means
If you repeated the sampling many times, about 95% of the 95% intervals built this way would contain the true mean. For small samples with an estimated standard deviation, a t interval is slightly wider.
Questions
What z is used for 95%?
1.959963985.
Why is a 99% interval wider?
More confidence needs a wider net.
Formulas
CI = x̄ ± z × σ ÷ √n
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).