Power Analysis Calculator
Calculate statistical power for a given effect size and sample size.
About Power Analysis Calculator
Required sample size scales with the inverse square of effect size, so detecting a half-size effect needs four times the participants. Eighty per cent power is the conventional minimum. Underpowered studies waste resources and produce unreliable literature, because the significant results that do emerge are disproportionately overestimates.
Formula
Power Analysis
Power = P(reject H₀ | H₁ true); required n per group ≈ 2(z_α + z_β)² ÷ d²
- power
- Probability of detecting a real effect of the specified size
- type II error
- Failing to detect a real effect, equal to 1 − power
Worked example
With the default values below, Power Analysis Calculator returns Statistical Power of 81.418%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Effect sizeaccepts 0.01–5
- 0.5
- Sample size per groupminimum 2
- 64
- Significance levelaccepts 0.1–20 %
- 5 %
Results
- Statistical Power
- 81.418%
- Type II Error Rate
- 18.582%
- Sample Size per Group for 80 Per Cent Power
- 63
- Sample Size per Group for 90 Per Cent Power
- 85
- Verdict
- Adequately powered
Step by step
- 1Values used
- 2Power Analysis
- 3Statistical Power= 81.418
- 4Type II Error Rate= 18.582
- 5Sample Size per Group for 80 Per Cent Power= 63
- 6Sample Size per Group for 90 Per Cent Power= 85
- 7Verdict= Adequately powered
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Power Analysis calculated?
Power = P(reject H₀ | H₁ true); required n per group ≈ 2(z_α + z_β)² ÷ d² Required sample size scales with the inverse square of effect size, so detecting a half-size effect needs four times the participants. Eighty per cent power is the conventional minimum.
Why does Power Analysis matter?
Underpowered studies waste resources and produce unreliable literature, because the significant results that do emerge are disproportionately overestimates.
What values do I need to enter?
This calculator takes 3 inputs: Effect size, Sample size per group, Significance level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.