Standard Deviation CalculatorFree online math calculator — instant results, no sign-up

x̄ = (Σ x_i) / n
s = √[ Σ (x_i - x̄)² / (n - 1) ]
σ = √[ Σ (x_i - μ)² / N ]
s² = Σ (x_i - x̄)² / (n - 1)

• x_iIndividual data value in the dataset
• n, NTotal count of observations in the sample or population
• x̄, μArithmetic mean of the sample or population
• sSample standard deviation (using Bessel's correction, n − 1)
• σPopulation standard deviation (divided by N)
• s²Sample variance

The calculator parses the input string into a list of numbers and determines the count. It computes the mean, sums the squared deviations from that mean, and divides by n − 1 for sample metrics or by N for population standard deviation. Final floating-point values are rounded to 6 decimal places.

These are the calculator's starting values and the results it actually produces for them.

1. 1Parse the input values into an array of individual numbers and count them.
2. 2Add all values together and divide by the count to determine the arithmetic mean.
3. 3Subtract the mean from each number, square the resulting differences, and sum them.
4. 4Divide the sum of squared differences by n − 1 (or N for population) and take the square root.

Further reading

• Khan Academy: Summarizing Quantitative Data