# Standard Deviation Calculator

URL: https://speedycalculator.com/calculators/statistics/standard-deviation/
Last updated: 2026-10-25

> The standard deviation calculator finds the sample and population standard deviation of a list of numbers, along with the variance, mean and count. Paste values separated by commas, spaces or new lines.

## Inputs

- Data

## Results

- Sample standard deviation (s)
- Population standard deviation (σ)
- Sample variance
- Mean
- Count

## Formula

```
Sample s = √(Σ(x − x̄)² ÷ (n − 1))
Population σ = √(Σ(x − μ)² ÷ n)
```

## Explanation

Standard deviation measures how spread out values are around the mean. A small value means data cluster tightly; a large value means they are widely scattered.

### How to use the Standard Deviation Calculator

- **Data**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Subtract the mean from each value, square the differences, add them, divide by n − 1 (sample) or n (population) and take the square root.

### What each result means

- **Sample standard deviation (s)** = stdev([Data])
- **Population standard deviation (σ)** = pstdev([Data])
- **Sample variance** = variance([Data])
- **Mean** = mean([Data])
- **Count** = count([Data])

## Worked example

Inputs — Data: 4, 8, 15, 16, 23, 42.

Results — **Sample standard deviation (s) = 13.4907**; Population standard deviation (σ) = 12.3153; Sample variance = 182; Mean = 18; Count = 6.

## Key terms

- **Variance**: The square of the standard deviation.

## FAQ

**Sample or population?**
Use sample (n − 1) when your data are a sample from a larger group; population when you have every value.

**Why n − 1?**
It corrects the bias of estimating spread from a sample (Bessel’s correction).

**What formula does the Standard Deviation Calculator use?**
Sample s = √(Σ(x − x̄)² ÷ (n − 1)).


## Sources

- [NIST/SEMATECH e-Handbook of Statistical Methods](https://www.itl.nist.gov/div898/handbook/)