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🔭 Sample Size Calculator

Determine the required sample size for surveys and research studies. Choose between unknown and known population size with confidence level and margin of error controls.

Use 0.5 if unknown (most conservative)

Sample Size Formulas

Unknown Population
n = (z² × p × (1−p)) / e²
Known Population (Finite Correction)
n_adj = n / (1 + (n−1) / N)
Z-values
90% → z=1.645 | 95% → z=1.96 | 99% → z=2.576

How to Choose the Right Sample Size

  1. 1
    Set Margin of Error
    Smaller margins (e.g. ±3%) require larger samples. For most surveys, ±5% is a practical balance.
  2. 2
    Choose Confidence Level
    95% is the industry standard. 99% gives more certainty but demands a larger sample.
  3. 3
    Estimate Population Proportion
    If unknown, use p=0.5. This maximises the required sample and ensures you won't undersample.
  4. 4
    Apply Finite Correction
    If your population is small and known, use the finite correction formula to reduce the required sample size.

Worked Example

A researcher wants a 95% CI, ±5% margin, and estimates p=0.5.

n = (1.96² × 0.5 × 0.5) / 0.05²
n = (3.8416 × 0.25) / 0.0025
n = 0.9604 / 0.0025
n = 385 (rounded up)

Frequently Asked Questions

Sample size is the number of individuals or observations selected from a population for a study. A larger sample produces more reliable and precise results, but at greater cost and time.

The margin of error quantifies the uncertainty in survey results. A ±5% margin at 95% confidence means the true population value is within 5 percentage points of your sample result 95% of the time.

Higher confidence levels require larger samples. Increasing from 95% to 99% confidence increases the required sample by roughly 75% while keeping margin of error constant.

p is the estimated fraction of the population with a specific characteristic. Using p=0.5 maximises the required sample and is the safe default when you have no prior data.

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