Standard Deviation Calculator

Calculate standard deviation, variance, mean, median, min, max and range from a set of numbers.

Last updated: April 2026 · Source: BBC Bitesize — Standard deviation

Std Dev (Population)

4.8990

Std Dev (Sample)

5.2372

Mean

18

Median

18.5000

Count

8

Sum

144

Min

10

Max

23

Range

13

Disclaimer

This calculator is provided for informational purposes only and should not be considered as financial or tax advice. All calculations are performed locally in your browser — no personal data is collected or sent to our servers. Rates and thresholds are sourced from HMRC and GOV.UK and are updated for the current tax year. Always verify results with HMRC or consult a qualified professional before making financial decisions.

How It Works

Standard deviation measures how spread out values are from the mean (average) of a data set. A low standard deviation means values cluster tightly around the mean, while a high standard deviation indicates wide dispersion. It is one of the most commonly used statistics in science, business and social research.

The calculator computes both population standard deviation (σ) and sample standard deviation (s). The sample version divides by n−1 (Bessel's correction) to give an unbiased estimate when your data is a subset of a larger population. It also shows variance, mean, range and sum.

Enter your numbers separated by commas or spaces. The calculator handles data sets of any size and displays each step of the calculation: mean, deviations from mean, squared deviations, sum of squares and the final standard deviation.

Example: Data set {4, 8, 6, 5, 3}

  1. Mean: (4+8+6+5+3) ÷ 5 = 5.2
  2. Deviations: −1.2, 2.8, 0.8, −0.2, −2.2
  3. Squared deviations: 1.44, 7.84, 0.64, 0.04, 4.84
  4. Population std dev (σ): √(14.8 ÷ 5) = 1.72
  5. Sample std dev (s): √(14.8 ÷ 4) = 1.92

Source: BBC Bitesize — Standard deviation

Frequently Asked Questions

What does the Standard Deviation Calculator do?
Calculate standard deviation, variance, mean, median, min, max and range from a set of numbers. All calculations are performed in your browser using official UK rates and thresholds.
How accurate are the results?
This calculator uses standard mathematical algorithms and provides results accurate to the precision shown. For very large numbers or high-precision requirements, results are rounded to a reasonable number of decimal places.
Can I use this for schoolwork?
Yes. This calculator is suitable for GCSE, A-level and university-level mathematics. It follows standard mathematical conventions used in UK education.