Universal Calculator
TAIIR

Sample Size Calculator

Determine the ideal sample size for your survey or research study. Set your confidence level, margin of error, and population size.

Use 50% if unknown (worst case)
Leave empty for very large populations

Recent

No calculations yet

Mastering Sample Size Determination: Complete Guide

Sample size is a critical element of any survey or experiment. It determines the precision of your estimates and the statistical power of your conclusions. This Professional Sample Size Calculator helps you find the minimum number of respondents needed to achieve a desired margin of error and confidence level, or conversely, compute the margin of error given a sample size. It supports both infinite and finite populations using the standard Cochran formula with finite population correction (FPC).

The Sample Size Formula

For an infinite population, the required sample size n is given by n = (Z² × p × (1−p)) / E², where Z is the z‑score for the confidence level, p is the estimated proportion (use 0.5 for most conservative), and E is the margin of error. When the population is finite and the sample represents more than 5% of it, the finite population correction reduces the required size: n_adj = n / (1 + (n−1)/N).

💡 Example

For 95% confidence (Z=1.96), 5% margin of error, and p=50%, the required sample size for an infinite population is 385. If the total population is 2,000, the adjusted sample size drops to 323.

Choosing Confidence Level and Margin of Error

Common confidence levels are 90%, 95%, and 99%. A higher confidence level requires a larger sample. The margin of error (e.g., ±5%) indicates the range within which the true population value is expected to lie. Halving the margin of error quadruples the required sample size—a key trade‑off in survey design.

Finite Population Correction (FPC)

When your population is small (typically under 10,000), the FPC adjusts the sample size downward because sampling without replacement reduces variability. The calculator automatically applies this correction when you enter a finite population size.

Frequently Asked Questions

What if I don't know the population proportion?

Use 50% (0.5). This maximizes p(1−p) and yields the largest, most conservative sample size.

How does sample size affect margin of error?

Margin of error is inversely proportional to the square root of sample size. Doubling the sample size reduces the margin of error by a factor of √2 ≈ 1.414.

When should I use finite population correction?

Apply FPC when your sample size is more than 5% of the total population. The calculator does this automatically when you provide a population size.

What is a good sample size for a survey?

A sample of 385 is standard for 95% confidence and 5% margin of error for large populations. For smaller populations, the calculator will suggest a smaller number.

Related Tools

Protein CalculatorLoan CalculatorBac CalculatorProfit Margin CalculatorFha Loan CalculatorApr Calculator