Confidence Interval Calculator for Conversion Rate

This tool shows the band of uncertainty a rate hides: the confidence interval. It has two modes. In the first, you enter conversions and visitors and see the interval of the conversion rate itself (with Wilson or Wald). In the second, you enter A and B and see the interval of the difference between them in percentage points. If what you want is the direct business verdict (who won, p-value and lift), use the statistical significance calculator: it answers "can I switch the page?". This one answers "how precise is my measurement?".

How to use it

1. Pick the mode: one rate (the interval of a single conversion) or difference between A and B.
2. Pick the confidence level: 90%, 95% (default) or 99%.
3. In one-rate mode, enter conversions and visitors and pick the method (Wilson recommended).
4. In difference mode, enter visitors and conversions for A and for B.
5. Read the point estimate and the lower and upper bounds. In the difference, check whether the interval crosses zero.

How it works: the formulas

For one proportion, the Wilson method (default) is far more accurate than the classic Wald formula when the rate is low or the sample is small:

Where p̂ is the observed rate (conversions over visitors), n the number of visitors and z the normal critical value (1.96 for 95%). The interval runs from center minus half to center plus half. For the difference between two rates, the interval is (p̂B − p̂A) plus or minus z times the standard error √( p̂A(1−p̂A)/nA + p̂B(1−p̂B)/nB ).

Worked example (reproduces the default result)

With the values already filled in one-rate mode: 120 conversions in 2,000 visitors, so p̂ = 6.00%, and z = 1.96 for 95%. The Wilson center is (0.06 + 3.8415/4,000) / (1 + 3.8415/2,000) = 0.06084. The half is (1.96/1.00192) · √(0.06·0.94/2,000 + 3.8415/(4·2,000²)) = 1.9562 · 0.005333 = 0.01043. So the interval runs from 0.06084 − 0.01043 to 0.06084 + 0.01043, that is, from 5.04% to 7.13%, exactly what the tool shows when it opens.

Switching the method to Wald, the same data gives 6.00% plus or minus 1.96 · √(0.06·0.94/2,000) = 6.00% plus or minus 1.04pp, that is, from 4.96% to 7.04%. Notice that the Wilson interval is slightly shifted up and a bit wider: that correction at the extremes is what makes it the preferred method. In difference mode, with A at 5.00% (100/2,000) and B at 6.50% (130/2,000), the +1.50pp difference comes with a 95% CI of +0.06pp to +2.94pp: since it does not include zero, the difference is significant at 5%.

How to read it and where it misleads

The most common reading mistake is thinking "95% confidence" is the probability that the true value is in this interval. It is not: confidence is a property of the method across many repetitions, not a probability about this single interval. The second mistake is reading only the point and ignoring the width: a rate of 6% measured with 50 visitors has an interval so wide it decides nothing. Before concluding anything, look at the bounds, not just the center.

In difference mode, an interval that crosses zero is the sign that you cannot yet claim who is better, nor that they tied: almost always the sample is short. To know how much sample your test needs, use the sample size calculator. And remember that a narrow interval far from zero is the ideal case: a real effect, well measured.

Good practice when reading an interval

The confidence interval is honest about uncertainty, as long as you read it right. Check these points.

• Always report the interval next to the point. A rate with no interval hides how much it can move.
• Use Wilson for proportions. Wald misleads when the rate is low or the sample is small.
• In A/B, check whether the difference interval crosses zero before declaring a winner.
• If the interval is too wide, collect more data. The width falls with the square root of the sample.

Frequently asked questions

What is a confidence interval, in one sentence?

It is the range of plausible values for the true population number, estimated from your sample. An observed rate of 6% with a 95% CI of 5.04% to 7.13% means the data are compatible with a true rate anywhere in that range. The point alone misleads: the interval shows the uncertainty it hides.

What does "95% confidence" really mean?

It is not "a 95% chance the true value is in this specific interval". It is a property of the method: if you repeated the experiment many times and built the interval each time, about 95% of those intervals would contain the true value. The interval you hold either contains it or does not. The confidence is about the procedure, not about this single interval.

What is the difference between the Wilson and Wald methods?

Wald is the classic textbook formula (p̂ plus or minus z times the standard error), simple but poor when the rate is low, the sample is small or the result gets near 0% or 100%: in those cases it misses the coverage and can even go below 0 or above 100. Wilson fixes that, has much better coverage at the extremes and is the recommended default today. Use Wilson by default; Wald is here only for a teaching comparison.

Is a confidence interval the same as a significance test?

They are two sides of the same coin. If the 95% CI of the difference between A and B does not include zero, the difference is significant at 5%. The advantage of the interval is that it shows the plausible SIZE of the effect, not just a yes or no: a CI of +0.1pp to +0.3pp is significant but small; one of +2pp to +8pp is significant and large. For the ready business verdict, with p-value and lift, use the significance calculator.

Why does the interval shrink when I increase the sample?

Because the width of the interval falls with the square root of the sample size: to cut the interval in half you need four times more data. That is why rates measured with few visitors come with huge intervals and decide nothing. If your interval is too wide, the problem is almost never the formula: it is the lack of sample.

Keep going

Understood the uncertainty? The next step is the business verdict, with p-value and lift, in the significance calculator. For the p-value on its own, see the p-value calculator. The concept behind it is in the guide A/B testing statistical significance.