Sample Size Calculator

To determine how many subjects you need to survey, the calculator applies standard statistical formulas based on the normal distribution. The core formula for infinite populations is: n = (Z² × p × (1 - p)) / E², where n represents the sample size, Z is the Z-score corresponding to your desired confidence level, p is your estimated population proportion, and E is the margin of error. When surveying a finite population, the tool applies a population correction factor to adjust the final sample size downward without losing statistical power: n_adjusted = n / (1 + (n / N)), where N represents the total population size.

Imagine you want to survey customer satisfaction for a software platform with a user base of 10,000 people (Population N = 10,000). You choose a 95% confidence level, which translates to a Z-score of approximately 1.96. You estimate that 50% of users are satisfied (Proportion p = 0.5), representing maximum variability, and you want a 5% margin of error (E = 0.05). First, compute the infinite population sample size: n = (1.96² × 0.5 × 0.5) / (0.05²) = (3.8416 × 0.25) / 0.0025 = 384.16. Next, apply the finite population correction: n_adjusted = 384.16 / (1 + (384.16 / 10,000)) = 384.16 / 1.0384 ≈ 370. Therefore, you need to survey 370 users to achieve your statistical goals.

When planning your study, always use a 95% confidence level as a baseline standard for academic and business research unless higher stakes demand 99%. If you have no prior data regarding your population proportion, default to 0.5 (50%), as this creates the maximum possible variance and ensures your calculated sample size is large enough to handle any outcome. Finally, account for non-response rates by scaling your initial survey distribution upward by 10% to 20% to ensure you collect enough completed responses.