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Statistical Power Calculator

Estimate the statistical power of a two-sample test given effect size, sample size per group, and significance level.

Result

Statistical Power
60.9%
Interpretation
Underpowered (< 80%)

This uses a normal approximation for a two-sample, two-tailed test with equal group sizes - the widely used convention is that 80% power is the minimum acceptable for a well-designed study.

About the Statistical Power

This calculator estimates the statistical power of a two-sample test before data is collected, given an expected effect size, the planned sample size per group, and a chosen significance level. It is meant for planning studies or experiments where the goal is to know the chance of correctly detecting a real effect if one exists.

How It Works

You provide the expected effect size as Cohen's d, the sample size per group, and select a significance level of either 0.05 or 0.01. The calculator converts the significance level into a critical z-value, scales the effect size by the sample size to get a noncentrality-like term, and uses the normal distribution to estimate the probability of detecting the effect. It reports this probability as a percentage and states whether it meets the common 80% adequacy threshold.

zAlpha = inverse normal CDF of (1 - alpha/2). delta = d * sqrt(n/2). Power = 1 - normalCdf(zAlpha - delta) + normalCdf(-zAlpha - delta), clamped to the 0 to 1 range.

Formula & Methodology

This is a normal approximation for a two-sample, two-tailed test assuming equal group sizes in both arms. The alpha value comes from a fixed dropdown of 0.05 or 0.01, converted to a two-tailed critical z-value via the inverse normal CDF at 1 - alpha/2. The resulting power figure is clamped between 0 and 1 before being displayed as a percentage, and the calculator labels power at or above 80% as 'Adequately powered' and anything below as 'Underpowered'.

Examples

A moderate effect at a typical sample size

With an effect size of 0.5, a sample size of 40 per group, and alpha of 0.05, delta = 0.5 * sqrt(40/2) = 0.5 * sqrt(20) ≈ 2.236, and zAlpha ≈ 1.96, yielding a power estimate in the neighborhood of 80%, right at the conventional adequacy line.

A small effect with insufficient sample size

With an effect size of 0.2, a sample size of 40 per group, and alpha of 0.05, delta = 0.2 * sqrt(20) ≈ 0.894, which is well below zAlpha of 1.96, producing a power estimate far under 80% and labeled 'Underpowered'.

Advantages

  • Lets researchers check whether a planned sample size is adequate before running an experiment, rather than discovering low power after the fact.
  • Directly ties the significance level choice (0.05 or 0.01) into the power estimate, showing the tradeoff between stricter error control and detection ability.
  • Labels the result against the 80% convention automatically, giving an immediate adequacy read instead of just a raw percentage.

Common Mistakes

  • Plugging in an overly optimistic effect size that isn't grounded in prior data, which produces an inflated and unrealistic power estimate.
  • Assuming a study is well-powered just because the sample size is large, without checking whether the expected effect size is actually large enough to be detected at that sample size.
  • Treating power calculated after the fact from observed data ('post-hoc power') the same as prospective power calculated before data collection, which is a different and less meaningful use of the formula.

Edge Cases to Watch For

  • Sample size must be greater than zero or the calculator returns an error, since it appears inside a square root and division.
  • The result is clamped between 0% and 100% power even if the raw formula would produce a value slightly outside that range due to floating point behavior.
  • This is a two-tailed test approximation for equal group sizes; unequal group sizes or a one-tailed hypothesis are not modeled by this formula.

Common Use Cases

  • Researchers designing an experiment who need to justify a planned sample size before collecting data.
  • Analysts evaluating whether a completed or planned A/B test had enough participants per group to reliably detect the effect they cared about.
  • Students learning how effect size, sample size, and significance level interact to determine the probability of detecting a true effect.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

What is statistical power?

Power is the probability that a test correctly detects a real effect when one truly exists - it's 1 minus the probability of a false negative (Type II error). Low power means a study is likely to miss real effects, which is why power analysis is typically done before collecting data to decide on an adequate sample size.

Related calculators

Confidence Interval CalculatorCalculate the confidence interval for a sample mean.Sample Size CalculatorCalculate the minimum sample size needed for a survey or study at a given confidence level and margin of error.Margin of Error CalculatorCalculate the margin of error for a survey result given sample size and confidence level.Correlation Coefficient CalculatorCalculate the Pearson correlation coefficient between two paired sets of numbers.

Conclusion

Statistical power quantifies the chance of correctly detecting a real effect given a specific effect size, sample size, and significance level, and this calculator estimates it using a standard normal approximation for a two-sample test. Checking power before running a study helps avoid designs that are too small to reliably find the effect being investigated.