Study Size Calculator
Enter the outcome's standard deviation, the smallest difference worth finding, the significance level, the power and the expected dropout. The calculator gives the number of participants per group.
- Sample size
- Effect size
- Total
Take the standard deviation from a pilot study or past research.
n per group = 2(zα/2 + zβ)² ÷ d². With a standard deviation of 10 and a difference of 5, d is 0.5. At 5% significance and 80% power you need 63 per group, or 70 with 10% dropout.
Sample size chart
5% significance, two groups. Search for an effect.
| Effect d | 80% power | 90% power |
|---|---|---|
| 0.2 | 393 | 526 |
| 0.3 | 175 | 234 |
| 0.4 | 99 | 132 |
| 0.5 | 63 | 85 |
| 0.6 | 44 | 59 |
| 0.8 | 25 | 33 |
| 1 | 16 | 22 |
Per group.
Effect size and sample
5%, 80% power. Slide the effect.
Each dot is one participant or a group of them.
How to size a study
Effect to sample. Step through it.
Outcome
Choose the main one.
Register the sample size plan before you start.
Small, medium or large effect
Effect sizes. Compare them.
d 0.2.
d 0.5.
d 0.8.
Small effects need large studies.
Before you recruit
Study checks. Tick each item.
Tick each item as you go.
Ask a statistician to check unusual designs.
What you get
Study sizing. Each tile explains one result.
Sample.
Both groups.
d.
Percent.
Added.
An underpowered study can miss a real effect.
Frequently Asked Questions
No question matches that search.
How do I work out sample size for a study?
Use the standard deviation, the difference to detect, the significance and the power.
What is statistical power?
The chance the study finds an effect that is really there.
Why use eighty percent power?
It is a common balance between cost and the risk of missing an effect.
What is a standardised effect size?
The difference divided by the standard deviation, called Cohen's d.
How much should I add for dropout?
Divide by one minus the expected dropout rate.
Does this work for proportions?
No. Proportions use a different formula.
Studies that find the answer
Size the study before you start and your result is worth the effort.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.