Statistical Power Calculator

What this generator does

Computes power for a two-proportion test from the baseline rate, the relative effect and the sample size, then searches for the sample that reaches eighty per cent and shows how power rises across a range of sizes.

How to use this tool

1. Enter your current conversion rate.
2. Enter the relative improvement you want to be able to detect.
3. Set the sample size per variant.
4. Read the power, and the sample needed for 80%.

Understanding the controls

Baseline rate

The conversion rate you already have. Lower rates need much larger samples to detect the same relative change.

Effect to detect

A relative change: 20 means detecting a fifth improvement on the baseline. Smaller effects need dramatically more data.

Sample per variant

How many people each side would get. Power rises with the square root of this, so doubling the sample helps far less than halving the effect hurts.

Common use cases

• Working out how long an A/B test needs to run
• Checking whether a completed test had any chance of detecting the effect
• Deciding the smallest effect worth testing for
• Explaining why a small test that found nothing proves nothing
• Planning sample sizes before starting

How this generator works

Power is the chance the test statistic lands beyond the significance threshold when the effect is genuinely present. It follows from the difference between the two rates, their variances and the sample size, compared against the critical value for a five per cent two-sided test. Before display the power is confirmed to be a probability, the curve is confirmed to rise with the sample size and never fall, and the sample named for eighty per cent is checked to genuinely reach it.

Randomness and fairness

Nothing here is random. A baseline, an effect and a sample give exactly one power figure.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• This covers the two-proportion test only; continuous outcomes like revenue per visitor need a different calculation.
• Eighty per cent power is a convention rather than a rule — it means accepting a one in five chance of missing a real effect.
• The effect is entered as a relative change, and mixing that up with an absolute one is the commonest error here.
• Power says nothing about whether an effect of that size is worth having.

Privacy and your data

The power calculation runs in your browser. Your baseline rate, effect size and sample are never transmitted, stored or included in analytics.