Confidence Interval Calculator

About the Confidence Interval Calculator

A confidence interval gives you a range within which the true conversion rate likely falls, rather than a single point estimate. If your observed CR is 3.5% with a 95% CI of [3.1%, 3.9%], you can be 95% confident the true CR is somewhere in that range.

This calculator computes the confidence interval for a proportion (conversion rate) using the normal approximation. Enter your sample size and observed conversions, choose your confidence level (90%, 95%, or 99%), and get the lower bound, upper bound, and margin of error.

Confidence intervals are more informative than significance tests alone because they convey both the size of the effect and the uncertainty around it. They are essential for reporting A/B test results and for understanding the precision of your metrics.

When This Page Helps

Point estimates like "our conversion rate is 3.5%" hide the uncertainty inherent in any sample. This calculator reveals the range of plausible values, helping you make decisions that account for statistical uncertainty rather than treating estimates as exact.

How to Use the Inputs

1. Enter the total sample size (number of visitors or trials).
2. Enter the number of conversions (successes).
3. Select the confidence level (90%, 95%, or 99%).
4. Review the confidence interval bounds and margin of error.
5. A narrower interval indicates more precise measurement.

Example Calculation

Tips & Best Practices

• Wider intervals mean more uncertainty — you need more data for precision.
• The interval narrows proportionally to the square root of sample size (4× sample = 2× precision).
• Use 95% CI as the default. Switch to 99% for high-stakes decisions.
• When comparing A/B test variants, overlapping CIs do NOT necessarily mean no significant difference.
• Report A/B test results as CIs rather than just "significant/not significant."
• For very small samples (<30) or extreme rates (<1% or >99%), use Wilson or exact CIs instead.

Why Report Confidence Intervals

A single number like "3.5% conversion rate" implies false precision. A confidence interval communicates both the estimate and its uncertainty, enabling better decisions. Stating "3.5% ± 0.5% (95% CI)" gives stakeholders an honest picture of what the data supports.

Confidence Intervals in A/B Testing

For A/B tests, report the CI of the difference between variants, not just the individual CIs. The CI of the difference directly answers "how much better is B than A?" with the appropriate uncertainty. A CI for the lift of [2%, 18%] is much more actionable than "p < 0.05."

Sample Size and Precision

The margin of error is inversely proportional to the square root of the sample size. Practical implication: doubling your sample only reduces the CI width by 29%. To truly narrow uncertainty, you need patience (more data) or higher base rates (test on a macro-metric like add-to-cart instead of purchase).

Frequently Asked Questions

• What does 95% confidence mean?

  If you repeated the same experiment 100 times, approximately 95 of the resulting intervals would contain the true value. It does NOT mean there is a 95% probability the true value is in this specific interval (a common misconception).

• How do I narrow the confidence interval?

  Increase your sample size. The margin of error decreases with the square root of n. To halve the margin of error, you need 4× the sample. To shrink it by 10×, you need 100× the sample.

• What if the lower bound is negative?

  For proportions, clip the lower bound to 0%. This can happen with very small samples or very low conversion rates where the normal approximation is less accurate. For better accuracy in such cases, use the Wilson score interval.

• Can overlapping CIs still be significantly different?

  Yes. Two proportions' CIs can overlap by up to 25% and still be significantly different in a direct comparison test. Do not use CI overlap as a substitute for a proper significance test.

• Which confidence level should I use?

  95% is the standard for most business decisions. Use 99% for irreversible decisions or medical applications. Use 90% for exploratory analysis where you want to detect trends with less conservatism.

• Is this the same as the Wilson score interval?

  No. This calculator uses the Wald (normal approximation) interval, which is simpler and works well for moderate sample sizes and conversion rates between 5–95%. The Wilson interval is more accurate for small samples or extreme proportions.