Sample Size Calculator
Determine the exact number of survey respondents or test subjects required to achieve statistical confidence.
Required Sample Size
385
Infinite Population n
385
n = z² × p(1-p) / e²How to Use the Sample Size Calculator
- Select your target Confidence Level (90%, 95%, or 99%).
- Specify your acceptable Margin of Error (e.g. 5%).
- Optionally enter total Population Size (N) to apply finite population correction.
- Read the required sample size needed for your study.
Formulas & Principles
Infinite Population: n₀ = (Z² × p × (1 - p)) / e²
Finite Population Correction: n = n₀ / (1 + (n₀ - 1) / N)
Z critical values: 90% = 1.645, 95% = 1.96, 99% = 2.576
Frequently Asked Questions
What is Cochran's formula for sample size?
n₀ = (Z² × p × (1 - p)) / e², where Z is the critical value, p is estimated proportion (usually 0.5 for maximum variability), and e is the margin of error.
What is finite population correction (FPC)?
When sampling more than 5% of a finite population, FPC adjusts the required sample size down: n = n₀ / (1 + (n₀ - 1) / N).
Why is 95% confidence with a 5% margin of error common?
It offers an ideal balance between statistical rigor and achievable sample size (typically requiring ~384 respondents for large populations).
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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