Standard deviation and z-score calculator

Find the spread of a data set, or convert a value to a z-score and back.

More math tools

Quadratic equation solverRoots, vertex, and discriminantMatrix calculatorDeterminant, inverse, and productsLinear regressionBest-fit line, r, and R²Confidence intervalFor a mean, with z or tPermutations and combinationsnPr, nCr, and factorialsPercentage calculatorPercent of, change, and moreAll LabBench tools

Standard deviation

Standard deviation measures how far values typically sit from the mean. Use the sample version (divide by n − 1) when your numbers are a sample of a larger group, and the population version (divide by n) when you have every value.

Z-scores

A z-score says how many standard deviations a value is above or below the mean: z = (x − μ) ÷ σ. The percentile shown assumes a normal distribution and uses a numerical approximation that is accurate to about six decimal places.