Clinical Tools · Biostatistics · ICH E9
Clinical Trial Sample Size Calculator
Calculate required sample size for parallel group, two-proportion, and crossover clinical trials. Includes power analysis, dropout adjustment, and power curve table.
Core Formula — Two-Group Parallel (Continuous)
n = 2 × [(zα/2 + zβ)² × σ²] / δ²
δ = minimum difference to detect σ = pooled SD n = per group
zα/2 = 1.96 (α=0.05) zβ = 0.842 (power=0.80) zβ = 1.282 (power=0.90)
zα/2 = 1.96 (α=0.05) zβ = 0.842 (power=0.80) zβ = 1.282 (power=0.90)
Two-Group Parallel — Continuous Outcome
n per group
—
subjects
Total N
—
subjects
After Dropout Adj.
—
to enroll
Two Proportions — Binary / Event-Rate Outcome
n per group
—
subjects
Total N
—
subjects
NNT
—
number needed to treat
After Dropout Adj.
—
to enroll
Crossover Trial — Within-Subject Design
In a crossover trial each subject receives both treatments. This halves the required sample size by eliminating between-subject variability, but requires a stable condition and an adequate washout period.
n (crossover)
—
subjects (each receives both)
Parallel equivalent
—
total (parallel design)
After Dropout Adj.
—
to enroll
Common Scenario Reference Table
Minimum sample sizes per group for common effect sizes (two-sided α=0.05, power=0.80, σ=10, allocation 1:1):
| Standardized Effect Size (δ/σ) | Small (0.2) | Medium (0.5) | Large (0.8) | Very Large (1.0) |
|---|---|---|---|---|
| Power 70% | 124 | 21 | 9 | 6 |
| Power 80% | 197 | 32 | 13 | 9 |
| Power 85% | 246 | 40 | 16 | 11 |
| Power 90% | 313 | 51 | 21 | 14 |
Educational Purpose Only: These calculations are for planning and educational use. Final sample size must be confirmed with a qualified biostatistician and should account for interim analyses, adaptive design features, multiplicity corrections, and protocol-specific considerations (ICH E9, ICH E9(R1)).
Frequently Asked Questions
For a two-group parallel trial with a continuous outcome, use n = 2 × [(z_α/2 + z_β)² × σ²] / δ², where z_α/2 is the critical value for significance (1.96 for α=0.05), z_β is the critical value for power (0.842 for 80% power), σ is the pooled standard deviation, and δ is the minimum clinically important difference to detect. Always add 10–20% for expected dropout.
Statistical power (1−β) is the probability that the trial will detect a true treatment effect if one exists. Conventionally set at 0.80 (80%) or 0.90 (90%), higher power requires larger sample sizes but reduces the chance of a false-negative result (Type II error).
A crossover trial requires roughly half the subjects of a parallel trial because each subject serves as their own control, dramatically reducing within-group variability. The crossover formula uses within-subject SD rather than pooled SD. Crossover designs are not suitable for conditions that change over time or treatments with carryover effects.
NNT is the number of patients who need to receive a treatment for one additional patient to benefit compared to control. NNT = 1 / |p1 − p2|, where p1 and p2 are the event rates in control and treatment groups. An NNT of 5 means treating 5 patients produces one additional beneficial outcome.
Sample size calculations give the number of evaluable subjects needed to achieve the desired power. Since some enrolled subjects will drop out or have missing data, planned enrollment must be inflated. A 10–20% dropout adjustment is typical: adjusted N = calculated N / (1 − dropout rate).