Sample Size Calculator
Find how many people to survey (or measurements to take) for a chosen margin of error and confidence level.
Sample size needed
385
- Before rounding up
- 384.1458821
- Critical z
- 1.959963985
Show the work
Critical z for 95% confidence (two-sided)
z with 2.5% of the curve above it = 1.959963985
Sample size for a proportion
n0 = z to the power of 2 × p × (1 − p) ÷ E to the power of 2
1.959963985 to the power of 2 × 0.5 × (1 − 0.5) ÷ 0.05 to the power of 2 = 384.1458821
Round up to a whole number
n, rounded up
385
How it works
Proportion: n = z² p(1 − p) ÷ E²; mean: n = (zσ ÷ E)²; finite population: n ÷ (1 + (n − 1) ÷ N); always round up
Questions
- How does the sample size calculator work?
- Proportion: n = z² p(1 − p) ÷ E²; mean: n = (zσ ÷ E)²; finite population: n ÷ (1 + (n − 1) ÷ N); always round up.
- What do I need to enter?
- Estimating a, Confidence level, Margin of error (±), Expected proportion, Standard deviation (σ), Margin of error (±, same units), Population size. Optional fields can be left blank.
Related tools
- Margin of Error CalculatorFind the margin of error of a survey result or a sample mean at a chosen confidence level.
- Probability CalculatorCombine the probabilities of two events: both, either, neither, exactly one, and not A.
- Odds to Probability CalculatorConvert odds (for or against) to a probability, or a probability to odds.
- Combinations Calculator (nCr)Count the ways to choose r items from n when order doesn't matter — with or without repetition, exactly.
- Permutations Calculator (nPr)Count the ordered arrangements of r items taken from n — with or without repetition, exactly.
- Normal Distribution CalculatorFind the probability that a normally distributed value falls below, above, between or outside given values.
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