Study design · Power
Sample Size & Power Calculator
How many participants do you need — or how much power does the sample you have actually give you? For comparing two means or two proportions, and for a survey margin of error. With a power curve, and a blunt warning about the one power calculation you should never do after the fact.
Result
In plain English
Before you run a study, this tells you how many participants you need — or, for a sample you can afford, how good your chances are of catching a real effect.
- power
- The chance of detecting an effect if it's really there. 80% is the usual target; below that, real effects slip through too often.
- sample size (n)
- How many you need per group to reach that power.
- effect size
- How big a difference you're trying to detect. Smaller, subtler effects need much bigger samples.
- α (significance)
- The false-alarm rate you'll tolerate — usually 0.05.
- margin of error (surveys)
- The “give or take” on a survey estimate, e.g. ±3%.
- post-hoc power
- Power worked out after the fact, from the effect you happened to measure. It tells you nothing new — that's why the calculator warns against it.
Frequently asked
How big a sample do I need?
It depends on the effect size you want to detect, your significance level (usually 0.05), the power you want (usually 80%) and the variability of the outcome. Smaller effects and lower variability both demand larger samples — fill the inputs to see the trade-off.
What is statistical power?
The chance your study detects a real effect of a given size. 80% is the common target, meaning a 1-in-5 risk of missing a true effect (a Type II error). Underpowered studies waste effort and produce unreliable “null” results.
Why is post-hoc power misleading?
Computing “power” from your observed effect after a non-significant result just re-expresses the p-value — it adds nothing and can mislead. Power should be planned before the study, from the effect size you care about.
What is the margin of error, and how does it relate to sample size?
The margin of error is the half-width of a confidence interval — how far your estimate might sit from the truth. It shrinks with the square root of the sample size, so to halve it you need four times the data, not twice. That square-root law is why polls jump from 1,000 to a few thousand people but rarely to hundreds of thousands: past a point, each extra respondent buys very little precision.