Confidence Interval Calculator

Calculate 90%, 95%, and 99% confidence intervals for population means.

Z-Score

1

Percentile (below)

84.13%

Above percentile

15.87%

z = (75 − 65) / 10 = 1

Confidence Interval Calculator Formula & How It Works

CI = x̄ ± z*(σ/√n) | CI = x̄ ± t*(s/√n)
  • x̄ = sample mean
  • z* or t* = critical value for desired confidence level
  • σ = population SD (z-test) or s = sample SD (t-test)
  • n = sample size | SE = σ/√n = standard error

A 95% confidence interval means if you repeated the study 100 times, 95 of the resulting intervals would contain the true population mean. Use the z-distribution when n>30 or σ is known. Use t-distribution for small samples. The margin of error (±) decreases with larger sample size — quadrupling n halves the margin of error.

Confidence Interval Calculator FAQs

What does a 95% confidence interval mean?

If you collected 100 different samples and computed a confidence interval from each, approximately 95 of those intervals would contain the true population parameter. It does NOT mean there's a 95% chance the parameter is in THIS interval.

How does sample size affect confidence intervals?

Larger samples give narrower (more precise) confidence intervals because SE = σ/√n. Doubling n multiplies precision by √2 ≈ 1.41. To halve the margin of error, you need 4× the sample size. This is the fundamental trade-off in study design.

Related Calculators

Z-Score Calculator

Calculate z-score, percentile, and probability from any raw score in a normal distribution.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for any data set.

Sample Size Calculator

Find the minimum sample size for your survey or study with given confidence and margin of error.

P-Value Calculator

Calculate p-value from z or t statistics for hypothesis testing.