How to Calculate a Confidence Interval (With Conversion Rate Examples)

A single conversion rate hides how sure you can be about it. This guide shows how to calculate a confidence interval for a rate, a mean and the difference between two variants, with worked examples on conversion data and fixes for small samples.

What a confidence interval tells you

A confidence interval is a range around a measured value that probably contains the true value. "Conversion rate 4.5% (95% CI 3.86% to 5.14%)" says: from this sample, the real long-run rate is plausibly anywhere in that range.

More precisely, if you repeated the measurement many times, 95% of intervals built this way would contain the true value. It does not mean there is a 95% chance that this particular range contains it, but for everyday decisions, "the plausible range" is a fair reading.

The method in four steps

1. Compute the estimate: a mean, a rate, or a difference.
2. Compute its standard error (SE). This measures how much the estimate would vary from sample to sample. See standard deviation vs standard error.
3. Pick a confidence level and its multiplier: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
4. Interval = estimate ± multiplier × SE.

Formulas

The table below gives the standard error for the three cases you will meet most often.

Multipliers: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.

Example: a conversion rate

4,000 visitors, 180 conversions (sample numbers).

• Rate p = 180 ÷ 4,000 = 4.5%
• SE = √(0.045 × 0.955 ÷ 4,000) ≈ 0.00328, or 0.328 percentage points
• 95% interval = 4.5% ± 1.96 × 0.328 = 4.5% ± 0.64 points, so 3.86% to 5.14%

A higher confidence level widens the range: 3.96–5.04% at 90%, 3.66–5.34% at 99%.

Example: the difference between two variants

Variant A converts 180 of 4,000 (4.5%); variant B converts 212 of 4,000 (5.3%).

• Difference = 0.8 percentage points
• SE = √(0.045 × 0.955 ÷ 4,000 + 0.053 × 0.947 ÷ 4,000) ≈ 0.483 points
• 95% interval = 0.8 ± 1.96 × 0.483, so −0.15 to +1.75 points

The interval includes zero, so the data is consistent with no real difference. B may well be better, but this sample cannot rule out that it is not. That matches a two-sided test at the 5% level not being significant; see statistical significance.

Small samples

• Rates with few conversions. With 3 conversions in 40 visitors (7.5%), the simple formula gives −0.66% to 15.66%: a negative rate is impossible. Use the Wilson interval instead, which gives about 2.58% to 19.86%. Most statistics libraries and online calculators offer it.
• Means from small samples. Use the t distribution instead of 1.96. For 25 sessions with a mean of 12.4 minutes and a standard deviation of 6.0, SE = 6.0 ÷ 5 = 1.2, t = 2.064, so the 95% interval is 9.92 to 14.88 minutes.

How to read and report intervals

• Width matters as much as the centre. "4.5% ± 0.64" and "4.5% ± 3" are very different findings.
• Overlapping intervals do not prove "no difference". Compute the interval of the difference directly, as above.
• Report the level. Always say 90%, 95% or 99%.
• Intervals only cover sampling noise. Bot traffic, broken tracking or a holiday week are not inside the ± range.

To plan how many visitors you need for a narrow enough interval, see minimum detectable effect.

Getting the counts from TapCub

For a rate you need two numbers: conversions and the base. Take them from Web analytics › Goals (conversions and visitors for a goal) or from the step counts of a funnel in All-platform analytics. Use the same date range and filters for both variants. For a mean, use All-platform analytics › Behavior › Behavior analysis with an average aggregation on the property. Then apply the formulas above.

See also: Central limit theorem.