Confidence Interval Calculator
Get a confidence interval for a sample mean (using the t-distribution) or for a proportion (normal approximation), with the margin of error.
95% interval
69.266 – 75.534
Margin of error
± 3.134
Critical t
2.0227
df = 39
Formula: mean ± t × s ÷ √n. If you repeated this sampling many times, about 95% of intervals built this way would contain the true population mean.
How to use the Confidence Interval Calculator
- 1Choose a mean or a proportion.
- 2Enter your sample statistics and choose a confidence level.
- 3Read the interval and the margin of error.
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the sampling many times, about 95% of intervals built this way would contain the true value. It doesn't mean a 95% chance that this particular interval does.
Why use the t-distribution for a mean?
When the population standard deviation is estimated from the sample, the t-distribution accounts for that extra uncertainty — especially with small samples.
When is the normal approximation for proportions unreliable?
When there are fewer than about 10 successes or 10 failures. Use a Wilson or exact interval instead.
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