How is the margin of error calculated?

Multiply 1.96 by the square root of p(1−p)/n, where p is the observed rate and n the sample size. At 4% on 5,000 samples it is about ±0.54 points.

What does a 95% confidence interval mean?

If you repeated the measurement many times, about 95% of the intervals produced would contain the true rate. It expresses precision, not certainty about any single result.

How much sample do I need to halve the margin?

Four times as much. Precision improves with the square root of sample size, so each halving of the margin costs a quadrupling of sample.

Can I compare two rates using intervals?

Roughly — substantial overlap means the data cannot separate them. For a proper comparison use a two-proportion significance test rather than eyeballing intervals.

Calculator · 115

Confidence Interval Calculator

See how precise a measured rate really is — and decide whether the sample supports the decision you want to make.

Observed conversion rate

Sample size

sample

Margin of error (95%)

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Average

Scenario lens Current · Benchmark · Optimized

Leverage

Formula

Margin of error ≈ 1.96 × √(p(1 − p) / n)

Understanding confidence intervals

Reference material — the calculator above stays the primary tool.

What a confidence interval measures

A confidence interval is the range within which the true conversion rate most likely sits, given what a sample observed. The margin of error is its half-width: at 95% confidence, the true rate falls within this distance of your measured rate about nineteen times in twenty.

It is the antidote to false precision. A rate measured as 4.0% is never exactly 4.0% — it is 4.0% give or take, and the interval says how much.

How to read your result

The result is the margin of error in percentage points, with a smaller interval marked stronger. The scenario lens then shows the sample size that tighter precision would require.

Strong — a tight interval; the rate is well pinned down. Average — usable but loose. Low — wide; the sample cannot support fine distinctions.

Precision costs sample

Halving the margin needs four times the sample. Treat these as orientation.

Context	Typical median
Small sample	Wide interval, weak reads
4\u00d7 the sample	Half the margin
Low base rates	Need more sample
Overlapping intervals	No reliable difference

Using intervals well

Compare intervals, not point estimates. If two variants' intervals overlap substantially, the data cannot separate them no matter how different the headline rates look. Model a tighter margin as a scenario above to size the sample required.

Intervals in context

Read this alongside the significance and sample size tools, which the related tools cover. The interval describes precision on one rate; significance testing compares two, which is the question most experiments actually ask.