Statistics

Confidence Interval Calculator

Calculate confidence intervals for a mean or a proportion — choose your confidence level (90%, 95%, 99% or custom), and see the margin of error and lower and upper bounds.

Formula
CI = x̄ ± z × (s ÷ √n)

Enter your values

Enter a valid sample mean.
Enter a valid SD (greater than 0).
Enter a sample size of at least 2.
Enter a confidence level between 50 and 99.99.
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Ready to calculate

Enter your values on the left, then press Calculate.

Margin of error
±
Lower bound
Upper bound
Confidence width
What this means

How it works

Understanding Confidence Interval

1

What a CI tells you

A 95% confidence interval gives you the range that the true population value is likely to fall within, with 95% confidence. Wider intervals mean more uncertainty; narrower intervals mean more precision — but require larger sample sizes.

2

Mean vs proportion

For continuous data (heights, weights, cycle times) use the mean mode. For pass/fail or yes/no data (defective rate, conversion rate, customer satisfaction %) use the proportion mode — the maths is different.

3

The cost of confidence

Going from 95% to 99% confidence widens your interval by about 30% — meaning more uncertainty for the same data. To narrow the interval, the only lever is sample size: doubling n cuts the margin of error by about 30%.