RandoziConversion Rate Comparison Calculator
Enter the number of visitors (trials) and conversions (successes) for variants A and B. You get each rate, the gap in percentage points, the relative gain of B over A and a 95 % Wilson interval for each rate, with a plain statement of whether the intervals overlap. It is a description of your numbers, not a verdict.
Variant A
Variant B
Difference, B minus A
+10 pp
| Variant | Rate | 95 % interval |
|---|---|---|
| Variant A40 of 100 | 40 % | 30.94 % to 49.8 % |
| Variant B50 of 100 | 50 % | 40.38 % to 59.62 % |
The 95 % intervals overlap.
This is not a significance test and not proof that one variant is better: each interval describes one rate on its own, and nothing here is computed for the difference between the two rates. Never read an overlap, or the lack of one, as a verdict.
Rate = successes ÷ trials. Relative gain = (rate B − rate A) ÷ rate A. Interval: Wilson score interval at 95 % (z = 1.96). Trials up to 1,000,000,000. Nothing you type leaves your browser.
How it works
- Type the number of trials and the number of successes for variant A.
- Do the same for variant B. Successes cannot exceed trials.
- Read the rates, the difference in percentage points and the relative gain.
- Look at the two intervals and whether they overlap, then copy the summary to share it with its caveat.
What people use it for
Two versions of a landing page
Put the visitors and sign-ups of each version side by side and see how big the gap is, and how wide the uncertainty is.
Email subject lines
Compare the share of opens or clicks of two subject lines sent to similar lists.
Sanity-checking a report
Rebuild the rates and the points of difference quoted in a dashboard or a slide from the raw counts.
Questions
- How are the rates and the gap calculated?
- The rate is successes ÷ trials. The difference is rate B − rate A, shown in percentage points (pp). The relative gain is (rate B − rate A) ÷ rate A, which is not defined when the rate of A is 0 %. With 40 of 100 for A and 50 of 100 for B, the rates are 40 % and 50 %, the difference is +10 pp and the relative gain +25 %.
- What is the Wilson interval?
- It is a 95 % confidence interval for a proportion, built from p = successes ÷ trials, n = trials and z = 1.96: the centre is (p + z²/2n) ÷ (1 + z²/n) and the half-width is z × √(p(1 − p)/n + z²/4n²) ÷ (1 + z²/n). Unlike the simple p ± 1.96 × √(p(1 − p)/n), it stays between 0 % and 100 % and behaves well for small counts or rates near 0 % and 100 %.
- Does an overlap mean the variants are the same, and no overlap that one is better?
- No. This page does not run a significance test and never calls a variant a winner. Two intervals can overlap even when a proper test would find a difference, and the intervals describe each rate separately, not the gap between them. Randomisation, the planned sample size, repeated looks at the data and several variants all change what a result means. Use a dedicated test for a decision.
- What are the limits?
- Trials and successes must be whole numbers, successes cannot exceed trials, and trials go up to 1,000,000,000. The numbers are assumed to come from independent trials. Nothing you type leaves your browser.