Replicate & Sample Size Calculator
Plan the size of a comparative experiment. Choose a test family (one-sample, two-sample, or paired t-test), a target effect size, the desired statistical power, and the significance level. The calculator returns the minimum sample size per group and notes the assumptions of the normal approximation it relies on.
Calculator
Enter the planning parameters to see the required replication
Replicates per group
n = 2 × (z1−α/2 + z1−β)² × σ² / δ²
The standard two-sample normal approximation for comparing means with equal group sizes. The result is rounded up to a whole replicate. This is a planning estimate, not statistical advice for a specific study.
About this calculation
What this is
Sample size planning uses the normal approximation to the test statistic to determine how many observations per group are needed to detect a given effect with a chosen probability (power). The smaller the effect or the lower the power target, the larger the required sample.
Why it is used
Running too few samples misses real effects; running too many wastes resources and animals. Sample size planning lets the experimenter commit to a defensible n before the bench work begins.
Why this calculator exists
The normal-approximation formula is short, but the inputs (effect size, power, alpha, sidedness) are easy to mix up — particularly the difference between the two-sample test variance assumption (equal vs unequal). The calculator standardises the inputs and shows the per-group n.
Key assumptions
- The data approximate a normal distribution, or the test is robust to non-normality at the planned n.
- The variance estimate used in the power calculation is a credible stand-in for the real variance.
- The effect size is the smallest effect the experiment is intended to detect.
Limitations
- It uses the normal approximation, which is conservative for very small samples — the exact test may need fewer.
- It does not plan for attrition, dropout, or technical replicates — build those into the n.
- It does not replace a formal power analysis for non-standard tests (non-parametric, mixed models).
What this calculates
- Replicates per group
- Minimum whole replicates needed in each group (rounded up).
- Total replicates
- Replicates across both groups combined.
- Standardized effect size (d)
- δ / σ — the difference expressed in units of the standard deviation.
Frequently asked questions
What does this sample size calculator estimate?
It estimates the number of replicates per group needed to detect a difference between two independent means — for example treatment vs control on a plate or in a culture system — at a significance level and power you choose. It returns the minimum whole replicates per group (always rounded up), the total across both groups, and the standardized effect size d = δ / σ. This is a pre-study planning estimate using the standard two-sample normal approximation, not a post-hoc test of your data.
What inputs does the calculator need?
Four values: the smallest difference between the group means worth detecting (δ), in the outcome’s own units; an assumed standard deviation (σ), ideally from pilot data or the literature; a two-sided significance level (α), which must be between 0.001 and 0.2 with 0.05 the common choice; and a target power (1 − β), which must be between 0.5 and 0.999 with 0.8 the common choice. Underneath, it applies the normal-approximation formula n = 2(z₁₋α/₂ + z₁₋β)²σ²/δ².
What is statistical power in plain language?
Power is the probability that your experiment will actually detect the difference you specified, assuming that difference truly exists. At the common 80% target, you would still expect to miss a real effect of that size about one time in five, and the calculator shows the trade-off directly: raising the power target increases the replicates per group it returns. Power is the complement of the Type II error rate (1 − β), and this tool lets you set it anywhere from 0.5 to 0.999.
How many replicates do I need, and do technical replicates count toward that number?
There is no universal number: the honest answer depends on how small a difference you want to detect and how variable your assay is, which is exactly what the calculator derives from your δ, σ, α, and power. The replicates it plans for are the independent replicates behind the two-group comparison — averaging several technical measurements of the same sample does not substitute for more independent ones. The calculator also does not plan for technical replicates, attrition, or dropout, so build those into the n it gives you.
What are the limits of this estimate?
It uses the z (large-sample) approximation rather than the t distribution, so for fewer than roughly 30 replicates per group a t-test will require slightly more than the reported number — treat the result as a lower bound. It assumes two independent groups with equal replicate numbers and equal variance, an approximately normal outcome, a two-sided test, and a single comparison; multiple testing, paired designs, and unequal variances need different formulas. It is a planning aid, not statistical advice for a specific study — consult a statistician for confirmatory or clinical designs.
For research and educational use only. Not for clinical or diagnostic decisions. Always verify calculations independently before use in critical applications.