Power (sample size) calculators

Calculate how big your clinical trial needs to be with our easy to use online calculators

There are several different sample size calculators - choose the correct one according to the type of clinical trial you are planning (superiority/equivalence/non-inferiority) and the nature of the primary outcome variable (binary/continuous).

A superiority trial is one where you want to demonstrate that one treatment or intervention is better than another (or better than no treatment/intervention). An equivalence trial is where you want to demonstrate that a new treatment is no better or worse than an existing treatment and non-inferiority is to show that a new treatment is not worse than an existing treatment.

These calculators are based on approximations to the Normal distribution and may not be suitable for small sample sizes. These calculators have been tested for accuracy against published papers.

Binary outcome superiority trial

A binary outcome has two categories, such as dead/alive, hospitalisation - yes/no, therapeutic success/failure and so on. This calculator is designed for binary outcomes in parallel group superiority trials.

The percentage of patients that meet the primary outcome definition (e.g. percentage hospitalised) is compared between two randomised groups. You should power the trial to be able to detect the smallest clinically important difference between these percentages.


Adjustment for non-compliance/cross-over

You could say:

Technical note

Calculation based on the formula:

n = f(α/2, β) × [p1 × (100 − p1) + p2 × (100 − p2)] / (p2 − p1)2

where p1 and p2 are the percent 'success' in the control and experimental group respectively, and

f(α, β) = [Φ-1(α) + Φ-1(β)]2

Φ-1 is the cumulative distribution function of a standardised normal deviate.

Adjustment for cross-overs based on formula: nadj = n × 10,000 / (100 - c1 - c2)2
where c1 and c2 are the percent cross-over in the control and experimental group respectively.


Pocock SJ. Clinical Trials: A Practical Approach. Wiley; 1983.

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