What is statistical power and what value should I use?

Power is the chance of detecting a real effect of the size you specify. 80% is the conventional minimum; 90% is stronger and needs a larger sample. Power applies to comparison studies, not to simple estimation.

What effect size should I use?

Use the smallest difference that would be meaningful in your field — ideally from prior studies or a pilot. For two means you can enter Cohen's d, or a raw mean difference plus an SD. Guessing a large effect to shrink the sample is the most common way studies end up underpowered.

Home › Tools › Sample Size Calculator

How many participants do I need?

A free sample size calculator for the most common research designs. Set your effect, confidence, and power — get the number to recruit.

What are you doing?

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

Don’t have d? Enter a raw difference and SD instead:

Mean difference

Standard deviation

Proportion in group 1 (0–1)

Proportion in group 2 (0–1)

Standard deviation (expected)

Margin of error (±) in the same units

Expected proportion (use 0.5 if unsure — most conservative)

Margin of error (±) e.g. 0.05 for ±5%

Population size (optional — for a finite population correction)

Correlation to detect (r) (0–1)

Confidence level

Statistical power

Required sample size

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Now justify this number to your committee

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 to calculate sample size

Every sample size comes from four ingredients: the effect you want to detect (or the margin of error you can accept), your confidence level (how sure you want to be — commonly 95%), and, for comparison studies, your statistical power (the chance of detecting a real effect — commonly 80%). Bigger confidence and power, or a smaller effect, all push the number up.

Comparing two means: driven by Cohen’s d (or a mean difference ÷ SD), confidence, and power.
Comparing two proportions: driven by the two expected rates, confidence, and power.
Estimating one mean or proportion: driven by the SD (or expected proportion) and the margin of error you’ll accept.
Detecting a correlation: driven by the size of r you want to detect.
Always inflate for dropout: if you expect attrition, recruit more so the analysable sample still meets the target.

This calculator covers the common two-sided designs and is a planning aid, not a substitute for a formal power analysis on complex designs (clustering, repeated measures, survival, non-inferiority). For those, confirm with a statistician.

Frequently asked questions

How do I calculate sample size?

Choose your design, set the effect you want to detect (or the margin of error you can accept), your confidence level (commonly 95%), and — for comparisons — your statistical power (commonly 80%). The calculator converts those into the number of participants you need.

What statistical power should I use?

Power is the chance of detecting a real effect of the size you specify. 80% is the conventional minimum; 90% is stronger but needs a larger sample. Power applies to comparison studies, not simple estimation.

What effect size should I enter?

The smallest difference that would be meaningful in your field — ideally from prior studies or a pilot. Inflating the effect to shrink the sample is the most common route to an underpowered study.

Does this account for dropout?

No — it returns the analysable sample size. If you expect d% attrition, recruit n ÷ (1 − d/100).

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.

Which statistical test should I use? → Browse the books