Sample Size Calculator
Calculate the mathematically necessary sample size required to estimate a population proportion within a specified margin of error and statistical confidence level.
Total population being surveyed (leave large if unknown/infinite)
Likelihood that the true population value falls within margin of error
Acceptable range of sampling error (e.g. ±5%)
Minimum completed survey responses or participants required
How to Use This Calculator
- Enter the total population size (use 100,000+ if nationwide/unknown).
- Select your desired confidence level (95% is standard scientific convention).
- Set your acceptable margin of error (e.g. 5% or 3%).
- Review the required participant sample size.
Formula & Calculation Methodology
Cochran’s formula calculates initial sample size assuming maximum variability p = 0.5. The finite population correction (FPC) adjusts for bounded group sizes N.
Worked Example
Nationwide consumer survey: Pop 100,000+, 95% confidence, ±5% error
Small company survey: Pop 500 employees, 95% confidence, ±5% error
Frequently Asked Questions
Why does sample size level off around 384 for large populations?↓
As population N approaches infinity, the denominator (n₀ - 1)/N approaches 0. For 95% confidence and ±5% error, (1.96² × 0.25) / 0.05² ≈ 384.16 regardless of whether N is 100,000 or 1 billion.
What is the margin of error?↓
The margin of error quantifies sampling uncertainty. If a survey finds 60% agreement with a ±5% margin of error, the true population figure is between 55% and 65%.
Why assume p = 50%?↓
A 50/50 split produces the maximum mathematical variance p(1 - p) = 0.25, guaranteeing that the calculated sample size will be sufficient no matter the true distribution.
What is a limitation of theoretical sample size formulas?↓
This calculation assumes pure random sampling. It does not protect against non-response bias, leading questions, or voluntary response selection biases.
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Open calculator →Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.