Statistics

Sample Size Calculator

Determine the required sample size for a survey or study

Last reviewed: How we build & verify
%
%
Required Sample Size
—
Z-Value Used
1.96

How it works

Determines how many responses a survey needs for a target margin of error and confidence level. Getting this right before collecting data is what prevents a study that cannot answer its own question.

Formula
n = z² × p(1 − p) / e²
Finite population: n_adj = n / (1 + (n − 1) / N)
Variables
  • zcritical value for the confidence level (1.96 for 95%)
  • pexpected proportion; use 0.5 when unknown, which is the worst case
  • emargin of error as a decimal (0.04 for ±4 points)
  • Ntotal population size, if finite and small
Worked example
Inputs: 95% confidence, ±4% margin of error, unknown proportion
  1. z² = 1.96² = 3.8416
  2. p(1 − p) = 0.5 × 0.5 = 0.25
  3. 3.8416 × 0.25 = 0.9604
  4. e² = 0.04² = 0.0016
  5. 0.9604 / 0.0016 = 600.25, rounded up
Result: 601 responses
Notes
  • Population size barely matters until it is small. Polling a country of 300 million and a city of 300,000 both need about 1,067 people for ±3%; the correction only bites when N is under roughly 20,000.
  • This gives completed responses. Divide by the expected response rate to get how many people to contact: at a 20% response rate, 601 completions means inviting about 3,005.
  • If you plan to report results by subgroup, each subgroup needs its own adequate size. A 601-person survey split six ways gives roughly 100 per cell, with a margin of error near ±10 points.
  • Non-response bias is not fixed by a larger sample. A big skewed sample is worse than a small representative one, because it looks more credible while being just as wrong.

Related Tools

Anova CalculatorStatistics CalculatorAb Test CalculatorConfidence IntervalCorrelation CalculatorMargin Of Error

Most Searched Today

BMI CalculatorPercentage CalculatorCompound InterestMortgage CalculatorLoan EMI CalculatorCurrency ConverterSIP CalculatorAge CalculatorTip CalculatorLength ConverterCalorie CalculatorScientific Calculator

Frequently Asked Questions

Sample Size Calculator runs right in the browser tab you already have open. No install, no account, no cost.

Sample Size Calculator follows the standard method used in textbooks and technical references for this calculation, and we show the formula or approach on the page itself so you can check the working rather than trust a black box. Found an edge case that breaks it? Use the feedback button in the bottom-right corner.

Sample Size Calculator | ExaCalc