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math.sample-size-margin-error Calculator
Calculates the sample size required to achieve a target margin of error at a given confidence level for a proportion or mean. Margin of error is proportional to 1/√n — halving the margin of error requires four times as many observations.
Inputs
Margin Of Error Pct
The ± range around your estimate. Quadrupling the sample size roughly halves the margin of error.
Confidence Pct
How certain you want to be that the interval contains the true value. 95% is standard. Going to 99% widens the interval.
Population Size
Total number in the group you are studying. Matters for finite-population corrections when the sample covers a large fraction of the total.
Expected Proportion Pct
Reference formula or conversion factor shown for context.
Results
required sample size n
Sample size or count used in the calculation.
n for infinite population
The value at the specified point or condition.
z-score at
Number of standard deviations a value is from the mean. |z| below 2: within normal range. |z| above 2: in the outer 5% of the distribution. |z| above 3: in the outer 0.3%.
margin of error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
n = z²p(1-p)/E²
Sample size or count used in the calculation.
p=50%
Reference formula or conversion factor shown for context.