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SnapCalculations

Standard Deviation Calculator

Paste or type your numbers to get the standard deviation, variance and mean, with the full working from the mean to the square root.

Separate numbers with commas, spaces or semicolons.

Your data is a

Sample standard deviation

2.13809

Mean 5 · 8 numbers

Population SD (σ)
2
Sample variance (s²)
4.571429
Population variance (σ²)
4
Mean
5
Sum
40
Sum of squares
32

Step-by-step solution

Worked out with your numbers. Change any value above and the steps update.

  1. 1

    Mean: add the numbers and divide by how many there are

    40 ÷ 8 = 5

  2. 2

    Subtract the mean from each number and square the result

    (2 − 5)² = 9; (4 − 5)² = 1; (4 − 5)² = 1; (4 − 5)² = 1; (5 − 5)² = 0; (5 − 5)² = 0; … (2 more)

  3. 3

    Add up the squared differences

    sum of squares = 32

  4. 4

    Variance: divide by n − 1 (sample)

    32 ÷ 7 = 4.57142857

  5. 5

    Standard deviation: square root of the variance

    √4.57142857 = 2.13808994

How it works

  • Find the mean, then subtract it from each number and square the result.
  • Add the squared differences to get the sum of squares.
  • Variance = sum of squares ÷ n for a population, or ÷ (n − 1) for a sample.
  • Standard deviation is the square root of the variance.

Frequently asked questions

Should I use sample or population?

Use population when your numbers are the whole group you care about (every student in one class). Use sample when they are a subset used to estimate a bigger group (a survey). Most real-world data is a sample.

Why divide by n − 1 for a sample?

A sample's numbers sit closer to their own mean than to the true population mean, so dividing by n would underestimate the spread. Dividing by n − 1 (Bessel's correction) fixes that.

Results are estimates for general information and are not financial, medical or professional advice.