Confidence interval calculator

Calculate the confidence interval for a population mean given sample statistics.

Sample mean (x̄) Std deviation (σ) Sample size (n) Confidence

Confidence interval formula

CI = x̄ ± z × (σ/√n)

Where x̄ = sample mean, z = z-score for confidence level, σ = standard deviation, n = sample size.

Z-scores by confidence level

90%: z = 1.645. 95%: z = 1.960. 99%: z = 2.576.

What does it mean?

A 95% confidence interval means: if we repeated this sampling process many times, 95% of the intervals would contain the true population mean. It does NOT mean there's a 95% chance the true mean is in this specific interval.

Margin of error

E = z × (σ/√n). The margin of error decreases as sample size increases. To halve the margin of error, you need 4× the sample size.