How to Calculate Standard Deviation: A Step-by-Step Guide
Measures how spread out a list of numbers is.
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
What you need
- Numbers (separated by commas)
Step by step
- Enter the numbers (separated by commas).
- The results update as you type, or press Calculate.
- Read the sample standard deviation first, then the supporting figures below it.
The formula
s = √(Σ(x − x̄)² ÷ (n − 1)).
Worked example
For example, with these inputs:
- Numbers (separated by commas): 12, 15, 9, 22, 15, 30
the calculator returns:
- Sample standard deviation: 7.6267
- Variance: 58.1667
- Mean: 17.1667
Practical tips
- For exam work, show your method; marks are often given for working, not just the answer.
- When numbers are very large or small, scientific notation makes them easier to compare.
- Check your answer by working backwards from the result.
- Round only at the final step to avoid accumulated rounding errors.
Background
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
Related calculations
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- Binary to Decimal Converter: Converts binary to decimal.
- Hex to Decimal Converter: Converts hexadecimal to decimal.
- Area of a Circle Calculator: Calculates the area of a circle from the measurements you enter.
Want to skip the arithmetic? The free Standard Deviation Calculator does all of this instantly and updates as you type.
Run your own numbers: Standard Deviation Calculator