Conversion Rate Confidence Interval Calculator
Wald and Wilson confidence intervals for a proportion — the honest error bars around your conversion rate.
A conversion rate without an interval is half-truth. The Wilson interval is preferred over the textbook Wald (p ± margin) because Wald breaks for small samples or rates near 0%/100% (it can give impossible negative bounds). Report the Wilson interval; use Wald's margin only as a quick mental estimate.
Formula
Disclaimer: This tool is for general informational and estimation purposes only and is not professional financial, tax, accounting or legal advice. All figures are estimates — verify with a qualified professional before making decisions. Read the full disclaimer.
About Conversion Rate Confidence Interval Calculator
A reported conversion rate of '5.3%' is meaningless without error bars — from 1,000 visitors that rate could plausibly be anywhere in a range, and confidence intervals quantify exactly how wide. This calculator gives both the textbook Wald interval (p ± margin) and the more accurate Wilson interval, which stays valid for small samples and rates near 0% or 100% where Wald produces nonsensical negative or above-100% bounds. Use it to communicate honest uncertainty, to judge whether two rates really differ, and to know when a sample is simply too small to conclude anything.
How to use Conversion Rate Confidence Interval Calculator
- 1Enter your values into Conversion Rate Confidence Interval Calculator — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
- 2The result recomputes live using the formula shown on the page; there is no button to press.
- 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.
Why use Conversion Rate Confidence Interval Calculator?
- ✓Computes Conversion Rate Confidence Interval instantly in your browser — no sign-up, no upload, no server round-trip.
- ✓100% free and unlimited, with the exact formula shown: Wald: p ± z.
- ✓Runs entirely client-side, so every value you enter stays private on your device.
- ✓Live recompute as you type, with a worked example and authoritative references for trust.
Frequently asked questions
Why prefer the Wilson interval over the simple Wald one?+
The Wald interval (p ± z√(p(1-p)/n)) is taught everywhere but performs badly with small samples or extreme rates — it can extend below 0% or above 100%, and its real coverage is often far from the nominal 95%. The Wilson interval is asymmetric, respects the [0,1] bounds, and has reliable coverage across the full range, so it's the recommended default.
How does sample size affect the interval width?+
Width shrinks with √n — to halve the margin of error you need four times the sample. This is why early in a test the interval is huge and conclusions are premature, and why precise estimates of rare events (low rates) require very large samples. The interval is the honest picture the point estimate hides.
Can I use overlapping intervals to compare two rates?+
Cautiously — non-overlapping intervals do imply a significant difference, but overlapping intervals do NOT necessarily mean no difference (the test on the difference can still be significant even when individual intervals overlap somewhat). For comparing two variants, use the two-proportion z-test directly rather than eyeballing interval overlap.
What confidence level should I report?+
95% is the convention, balancing precision and certainty. 99% gives wider, more cautious bounds; 90% narrower but with more risk of excluding the true value. Match it to your other reporting (use 95% if your significance tests use α=0.05) so the interval and the hypothesis test tell a consistent story.
Related Statistics tools
A/B Test Significance Calculator
Two-proportion z-test for conversion experiments — p-value, confidence, relative lift and whether it's significant.
● LiveA/B Test Sample Size Calculator
Required visitors per variant to detect a target lift at your power and significance — before you launch.
● LivePermutation & Combination Calculator
nPr, nCr and n! for counting arrangements and selections — the foundation of combinatorics and probability.
● Live