Statistical Power Calculator
Whether your study is big enough to find the difference you are looking for, and how many people it would take.
Results
What this tool does
A study that is too small does not give a wrong answer; it gives no answer, and the cost is paid anyway. Power is the chance of detecting a real difference — eighty per cent is the usual minimum, meaning you would still miss it one time in five. Put in how large a difference matters to you, how many people you have in each group, and this page tells you the power you actually have and the number you would need to reach the power you want. Both figures are worth knowing before the first participant is recruited, not after the results come back ambiguous.
Formula
power ≈ 1 − Φ(critical z − d√(n÷2)) · n per group ≈ 2 ((z_α + z_β) ÷ d)²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
effect | Difference you want to catch (Cohen's d) | — |
n_per_group | People in each group | — |
alpha | Significance level | % |
tails | One tail or two | — |
target_power | Power you are aiming for | % |
OUT | Chance of finding it if it is there | % |
BE | Chance of missing it | % |
EN | That is enough | — |
NN | For your target you need, per group | — |
NT | Which is, in total | — |
HT | You have | — |
SH | Short by, per group | — |
EF | And that counts as | — |
CZ | z for that confidence | — |
Worked example
- Difference you want to catch (Cohen's d)0.5
- People in each group30
- Significance level5 %
- One tail or two2
- Power you are aiming for80 %
- Chance of finding it if it is there49.07 %
- Chance of missing it50.93 %
- That is enoughNo
- For your target you need, per group63
- Which is, in total126
- You have60
- Short by, per group33
- And that counts asMedium
- z for that confidence1.9600
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
Frequently asked questions
What is power, in plain words?
The chance that your study finds the difference, assuming the difference is really there. A power of 80 per cent means that if you ran the same study five times on a real effect, you would expect to miss it once. Underpowered studies are the quiet failure of a great deal of research: they do not produce wrong answers, they produce no answer, and the money and the participants are spent either way. Working this out before collecting data is the whole point; working it out afterwards tells you very little.
How do I choose the effect size?
Not by guessing, and not by using what a previous small study found — that figure is almost always inflated, because small studies only reach publication when they overshoot. The better question is how large a difference would actually matter to you, expressed as a fraction of the spread in your data. Cohen's rough labels of 0.2, 0.5 and 0.8 for small, medium and large are a starting point he himself described as a last resort, and the honest note here is that the sample size you get out is only as good as the number you put in.
How exact is the answer?
It uses the normal approximation to the two-sample t-test, which is what every published power table does. Above about twenty per group it agrees with the exact calculation to within a point of power; below that it runs slightly optimistic, so a very small study is a little weaker than this page suggests. It also assumes two groups of equal size, a continuous outcome and independent observations — a different design needs a different formula, not this one with the numbers adjusted.