Sample Size Calculator

Find how many responses you need for a survey at a given precision.

How the Math Works

The Sample Size Calculator uses the formula n = z² · p(1−p) ÷ MOE² to determine the minimum number of observations needed for reliable statistical analysis. The z-score reflects your desired confidence level (e.g., 1.96 for 95% confidence), p represents the estimated proportion of the population with the characteristic of interest (0.5 is commonly used to maximize variability), and MOE is the acceptable margin of error. This equation balances precision (smaller MOE requires larger samples), confidence (higher z-scores increase sample needs), and population variability to ensure statistically valid results.

Practical Applications

To apply this calculation, first determine your required confidence level (typically 90%, 95%, or 99%) and margin of error (e.g., ±3% or ±5%). For example, a market researcher wanting 95% confidence with a 4% margin of error would use z=1.96, assume p=0.5 for maximum sample size, then compute n = (1.96² × 0.5 × 0.5) ÷ 0.04² ≈ 240 respondents. Adjust p downward if prior studies suggest lower variability, and always round up to the nearest whole number to guarantee sufficient data collection.

Day-to-Day Use

This calculation helps you make confident decisions without wasting resources. When planning a customer satisfaction survey, a restaurant owner can quickly determine whether surveying 50 or 500 patrons provides meaningful insights. It’s equally useful for evaluating policy changes, testing product designs, or validating health study results—ensuring your conclusions are trustworthy while avoiding unnecessary data collection costs in everyday business or personal research projects.

Worked example

95%, ±5%, p 0.5 → 385.

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