Standard Deviation Calculator

Calculate standard deviation for sample and population data with steps.

The Standard Deviation Calculator computes how spread out your data is from the mean. It supports both sample and population standard deviation with detailed step-by-step solutions.

Enter your numbers in the input field
Choose between Sample (n-1) or Population (n) mode
The standard deviation is calculated automatically
Click "Show Steps" to see the detailed calculation process

Both sample (s) and population (σ) standard deviation
Step-by-step calculation with squared differences
Toggle between sample and population modes
Adjustable decimal precision
Summary panel showing all related statistics

When should I use sample vs population?: Use sample (n-1) when your data is a subset of a larger group. Use population (n) when you have data for the entire group.
Why does sample std dev divide by n-1?: Dividing by n-1 (Bessel's correction) gives an unbiased estimate of the population variance when working with a sample.
What does a standard deviation of 0 mean?: A standard deviation of 0 means all values in the dataset are identical.

Enter Data

Data Type

Decimals

Arithmetic Mean

x̄ = (Σxᵢ) / n

Median

Middle value of sorted data

Mode

Most frequent value(s)

Sample Standard Deviation

s = √[Σ(xᵢ - x̄)² / (n - 1)]

Sample Variance

s² = Σ(xᵢ - x̄)² / (n - 1)

Summary Statistics

Count -

Sum -

Min -

Max -

Range -

Mean -

Median -

Mode -

Std Dev (S) -

Std Dev (P) -

Variance (S) -

Variance (P) -

Q1 -

Q2 -

Q3 -

IQR -

Statistics Calculator

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