Sample Size & Power Calculator

Sample size to compare two means or two proportions at a chosen power, survey sample size for a margin of error with finite-population correction, and the power achieved by an existing n.

The Sample Size Calculator gives the number of subjects per group needed to detect a difference δ between means with standard deviation σ (n = 2[(z_α + z_β)σ/δ]²), between two proportions, or to estimate a proportion within a margin of error (n = z²p(1 − p)/e², with finite-population correction), plus the statistical power for a given n.

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How to use it

Choose the design.
Enter the effect you want to detect and the variability.
Set α and power.
Read n per group; inflate for dropout.

What you enter

Effect size inputs
α and power (or confidence and margin)

What you get

n per group
Total n
Standardised effect
Achieved power

Formula

n = 2 [ (z₁₋α/₂ + z₁₋β) · σ / δ ]²   |   n = z² p(1−p) / e²   |   n_fpc = n / (1 + (n − 1)/N)

Larger effects, smaller variability, higher α or lower power all reduce the required n. Power 0.80 and α 0.05 (two-sided) are conventional defaults.

Worked example

Input: δ = 5, σ = 10, α = 0.05 two-sided, power 0.80

Result: n = 63 per group (126 total)

Standardised effect 0.5 (medium) needs about 63 subjects per arm.

Questions

What power should I use?

0.80 is the conventional minimum; 0.90 is common for confirmatory trials. Higher power needs more subjects.

How do I choose the difference to detect?

Use the smallest difference that would matter scientifically or clinically, and the SD from a pilot study or the literature.

How many animals do I need?

Use the compare-means mode with the expected difference and SD from pilot data; ethics committees expect this calculation in the protocol.

Limitations

Normal-approximation formulas; for small n a t-based calculation gives slightly larger numbers.
Add 10–20 % for dropout and non-compliance.

References

Charan J, Biswas T (2013). How to calculate sample size for different study designs in medical research. Indian J Psychol Med 35:121-126.

More Statistics

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.