Confidence Interval Calculator

1. Enter the sample mean. This is the average of your sample data.
2. Enter the standard deviation. This is the population standard deviation (or sample std dev for large samples).
3. Enter the sample size (number of observations). Larger sample sizes give narrower intervals.
4. Select the confidence level. 95% is the most common. 99% gives a wider interval; 90% gives a narrower one.
5. Read the confidence interval. You can say you are 95% confident the true population mean falls between the lower and upper bounds.

CI = mean ± z × (σ / √n)

Where:
  mean = sample mean
  σ    = standard deviation
  n    = sample size
  z    = critical value for confidence level

Z critical values:
  90%  → z = 1.645
  95%  → z = 1.960
  99%  → z = 2.576

Standard Error: SE = σ / √n
Margin of Error: ME = z × SE

Example: mean=50, σ=10, n=100, 95% CI
  SE  = 10 / √100 = 10 / 10 = 1
  ME  = 1.960 × 1 = 1.960
  CI  = 50 ± 1.960 = (48.04, 51.96)

Interpretation: You are 95% confident that the
true population mean falls between 48.04 and 51.96.