Quickly estimate the number of subjects needed for your clinical study — proportions, means, group comparisons and non-inferiority tests. Sourced formulas, transparent calculation.
Survey, prevalence — a single measurement on a sample (e.g. % of patients responding to a treatment).
Method
Cochran: standard formula, recommended by default — precise and widely recognized in research. Slovin: simplified formula, faster but implicitly assumes a 50% proportion and a confidence level near 95% with no configuration — reserve for a very preliminary estimate, and requires a known finite population.
Estimated proportion
Your best estimate before the study (pilot study, literature, or 50% by default if you have no prior idea — this is the most conservative scenario, requiring the largest sample size).
%
Margin of error
Desired precision for your result. 5% is a standard in surveys. The smaller the margin, the larger the required sample.
%
Estimated standard deviation (σ)
Measure of the expected variability of your variable. Look for it in a prior study on a similar population — never invent it, as it has a direct and significant impact on sample size.
Acceptable margin of error
Desired precision for your result, in the same unit as the standard deviation.
Control group proportion (p1)
Expected value in the reference group (placebo, standard treatment), based on prior data or literature.
%
Treatment group proportion (p2)
Value you expect to observe in the experimental group. The difference from control should represent a clinically meaningful effect, not just a statistically detectable one.
%
Power (1-β)
Probability of detecting a real effect if it truly exists. 80% is the commonly accepted minimum. 90% is recommended if missing a real effect would have significant consequences (e.g. patient safety).
Common standard deviation (σ)
Measure of the expected variability of your variable. Look for it in a prior study on a similar population — never invent it, as it has a direct and significant impact on sample size.
Difference to detect
Smallest gap between the two groups that you consider important to detect. Do not artificially lower this value to reduce sample size — it must reflect genuine clinical relevance.
Power (1-β)
Probability of detecting a real effect if it truly exists. 80% is the commonly accepted minimum. 90% is recommended if missing a real effect would have significant consequences.
Subtype
Control group proportion
Expected value in the reference group, based on prior data or literature.
%
Common standard deviation (σ)
Measure of the expected variability of your variable. Look for it in a prior study on a similar population.
Non-inferiority margin (δ)
Maximum acceptable gap between the two treatments to conclude non-inferiority. This is NOT a statistical value — it must be defined upfront by a scientific or clinical committee, in agreement with regulatory authorities (FDA/EMA). Never choose it alone to artificially reduce sample size.
%
⚠ This margin must be validated by a scientific committee, never chosen alone.
Expected difference (Δ)
Real difference you anticipate between the two treatments. Enter 0 if you assume they are equivalent — this is the most conservative and common assumption.
Power (1-β)
ℹ️ One-sided test — confidence level is automatically adjusted (Z=1.645 for 95% one-sided).
Confidence level (α)
Probability of not being wrong if you conclude there is an effect. 95% is the standard in clinical research. 99% is stricter (safety study), 90% is more permissive (exploratory study).
Total population size
Leave blank if the population is very large or unknown (infinite population assumption). Only fill in if you are studying a closed, countable group (e.g. all patients at a given hospital).
Dropout / attrition rate
Percentage of participants you expect to lose during the study (withdrawal, unusable data). Base this on similar prior studies — 10-15% is common in multi-month clinical trials.
%
Final size to recruit
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participants
Preliminary estimate. Any sample size used in a regulatory protocol (FDA, EMA, ANSM) must be validated by a biostatistician and documented in the statistical analysis plan.
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Sources and methodology
Formulas from Cochran, W.G. (1977), Sampling Techniques, and Chow, S.C., Shao, J., Wang, H. (2008), Sample Size Calculations in Clinical Research — the standard reference work in clinical and regulatory biostatistics.
Need biostatistical validation?
Aigesis supports the definition and validation of your statistical analysis plans.