What this answers

This calculator answers "given the sample size I have (or am planning), how likely is my t-test to detect an effect of the size I expect?" the same underlying formula as this site's sample-size calculators, solved in the opposite direction: for power given n, rather than for n given a target power.

How it is calculated

Using the same normal-approximation design as the sample-size engines, this calculator computes the noncentrality implied by your effect size and sample size, then reads off the probability of correctly rejecting the null hypothesis at your chosen alpha. The one-sample and paired designs use the same formula (since a paired design is mathematically a one-sample test on the differences); the independent design accounts for the effect being split across two separate groups.

Worked example

For a paired design with a standardized effect of .5 and 32 pairs, at the conventional 95% confidence level, this calculator reports power just above 80%, consistent with 32 being exactly the sample size this site's own Sample Size for Paired Means calculator recommends for that same effect size and target power, a useful internal consistency check between the two engines.

Assumption audit

Calculated from your data: the achieved power given your entered design, effect size, sample size, and alpha.

Evidence to review: whether your assumed effect size reflects a realistic, ideally externally justified expectation rather than a number chosen simply because it produces a comfortable-looking power figure.

You must verify: which design genuinely matches your study: one-sample against a fixed benchmark, paired measurements on the same subjects, or two independent groups, since each implies a different formula here.

What this result does not mean

A high computed power does not guarantee your study will find a significant result; power describes the probability across many hypothetical repeated studies, not a certainty for this one. A low computed power for an already-completed study is a caution about how much weight to place on a non-significant result, not proof that no real effect exists.

Limitations

This calculator uses a normal approximation to the true noncentral t distribution a t-test actually follows, standard practice for planning purposes and reasonably accurate for typical sample sizes, though it can differ slightly from exact software output at very small n.