About

Conducting research without a calculated sample size is a gamble. If your sample is too small, your data lacks statistical significance (High P-Value). If it is too large, you waste resources. This calculator is designed for academic researchers, data analysts, and marketers who need to defend their methodology.

It employs Cochran's Formula with an integrated Finite Population Correction (FPC) factor. Unlike simplified tools, this application allows you to adjust the Population Proportion (p), essential for studies where you expect a specific split (e.g., 90/10) rather than the standard conservative 50/50. It also enables reverse engineering: calculating the Margin of Error achievable with a fixed budget/sample.

Formulas

We solve for n (sample size) using the standardized normal distribution.

1. Infinite Population:

n₀ = Z² p(1 - p)e²

2. Finite Population Correction (FPC):

Applied when n₀ > 5% of Population N.

n = n₀1 + n₀ - 1N

Where e is the Margin of Error (e.g., 0.05 for 5%) and p is the expected proportion (default 0.5).

Reference Data

Confidence Level	Z-Score (Z)	Alpha (α)	Application
99.9%	3.291	0.001	Genetic Research, Critical Safety
99%	2.576	0.01	Pharma, Medical Trials
95%	1.960	0.05	Standard Science & Business
90%	1.645	0.10	Political Polling
85%	1.440	0.15	Market Trends
80%	1.282	0.20	Pilot Studies

Frequently Asked Questions

A proportion of 50% yields the maximum possible sample size (worst-case scenario). This ensures your results are valid regardless of the actual distribution. If you know the split is likely 90% Yes / 10% No, entering 0.9 will significantly reduce the required sample size.

Leave the "Population Size" field blank. The calculator will assume an infinite population, which is statistically safe for any group larger than 20,000-50,000 individuals.

No. Standard Deviation measures data spread. Margin of Error measures the precision of your estimate relative to the true population value.