How do I calculate the power of my study?

Enter your design, your sample size, the effect size you want to detect, and your significance level (commonly 5% two-sided). The calculator returns the achieved power. Larger samples and larger effects give higher power.

What power is considered adequate?

80% is the conventional minimum and 90% is stronger. Below about 80%, a non-significant result is hard to interpret — you cannot tell a true null from an underpowered study.

What is post-hoc power?

Computing power from the observed effect after the fact ('observed power') is circular and discouraged. Use power based on a meaningful target effect size set from prior work — that is what this tool does.

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What statistical power does my study have?

A free power calculator for the most common research designs. Enter your sample size and the effect you want to detect — get your study's power.

What are you testing?

Effect size — Cohen’s d (0.2 small, 0.5 medium, 0.8 large)

Sample size per group

Effect size — Cohen’s d (mean difference ÷ SD)

Sample size (pairs, or total)

Proportion in group 1 (0–1)

Proportion in group 2 (0–1)

Sample size per group

Correlation to detect (r) (0–1)

Sample size (total)

Significance level (two-sided)

Achieved statistical power

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Get the free Sample-Size Justification Planner

A fill-in planner: choose the right type of power analysis, list its inputs, pick a defensible effect size, adjust for attrition, and draft the justification paragraph. We’ll email you the download link.

How statistical power works

Power is the probability of detecting a real effect of the size you specify. Four quantities are locked together — sample size, effect size, significance level (alpha), and power — fix any three and the fourth follows. This tool fixes sample size, effect, and alpha, and returns the power.

Two means: power rises with Cohen’s d and the number per group.
One-sample / paired mean: a within-subject design needs fewer participants for the same power.
Two proportions: driven by the gap between the rates and the per-group size.
Correlation: driven by the size of r and the total sample, via Fisher’s z.
Aim for 80% or more. Below that, a non-significant result is ambiguous.

A two-sided normal approximation suitable for planning. For complex designs (clustering, repeated measures, survival, non-inferiority) confirm with a formal power analysis or a statistician.

Frequently asked questions

What is statistical power?

The probability your study detects a real effect of the size you specify. Power of 0.80 = an 80% chance of finding it (and 20% chance of missing it, a Type II error).

What power should I aim for?

80% is the conventional minimum; 90% is stronger. Below ~80%, a non-significant result can’t be distinguished from an underpowered one.

Should I compute power after my study (post-hoc)?

Not from the observed effect — “observed power” is circular. Use a meaningful target effect set from prior work, which is what this tool does.

How do I increase power?

Recruit more participants, target a larger (still realistic) effect, use a within-subject/paired design, reduce measurement error, or accept a higher alpha.

Does it store anything?

No. The calculation runs entirely in your browser; nothing is uploaded or saved.

The workbook for this

The Sample Size & Power Analysis Workbook

“How many participants do I need?” — the answer, and the paragraph that proves it.

64 fill-in templates. Paperback $32.99 on Amazon

See inside the workbook

Just want the templates? The Sample Size & Power Analysis Template Kit: every template as a fillable PDF, $19.

How many participants do I need? → Which statistical test? →