Sample Size Calculator

Estimate sample size needed for a target margin of error.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

Estimate sample size needed for a target margin of error.

It combines Z Value, Estimated SD, Margin of Error to estimate Required Sample Size.

Formula & Method

Core equations: Proportion sample size:

n=\frac{z^2p(1-p)}{E^2}

(with finite-pop correction if used).

Notation used in the formulas: $R$ = Required Sample Size; $x_{1}$ = Z Value; $x_{2}$ = Estimated SD; $x_{3}$ = Margin of Error.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Reference Book

Introduction to Mathematical Statistics

Global Edition

Robert V. Hogg, Joseph McKean, and Allen T. Craig · Pearson

A standard reference for probability distributions, estimation, hypothesis testing, regression, and ANOVA.

View Book

Inputs Used

Z Value: Used directly in the calculation.
Estimated SD: Used directly in the calculation.
Margin of Error: Used directly in the calculation.

Related Calculators

Percentage Calculator - Perform common percentage operations: find a percentage of a value, calculate what percentage one number is of another, and find percentage change.
Fraction Calculator - Add, subtract, multiply, or divide two fractions and simplify the result.
Ratio Calculator - Simplify a ratio and compute equivalent forms.
Proportion Calculator - Solve proportions of the form a / b = c / x.
Average Calculator - Compute mean, median, and mode from up to five values.
Standard Deviation Calculator - Compute population and sample standard deviation from up to five values.
Prime Factorization Calculator - Factor an integer and derive divisor-count, divisor-sum, Euler totient, and divisor list.
GCD / LCM Calculator - Compute greatest common divisor and least common multiple of two integers.