Standard Deviation Calculator
Measure how spread out your data is. Paste your numbers and choose sample or population.
How to enter your data: Type or paste your numbers into the box, one after another, and separate each one with a comma, a space, or a new line (press Enter after each). Use plain numbers only, so no words, currency signs, or percent symbols; decimals such as 4.5 are fine.
Standard deviation is a single number that shows how spread out a set of numbers is. If it is small, most of your numbers sit close to the average; if it is large, your numbers are more scattered, with some much higher or lower than the average. This calculator works that number out for you from any list of values you enter, so you can see at a glance whether your results are consistent or varied.
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Where it is used
- Teachers: A teacher enters every mark from a class test to see whether the scores were bunched close together or spread widely apart.
- Small-business owners: A cafe owner enters the daily customer count for a month to see how much footfall changes from one day to the next.
- HR and customer-service staff: An HR manager enters staff satisfaction scores from a survey to check whether people mostly agree or opinions are split.
Sample vs population standard deviation
Use the sample standard deviation (dividing by n − 1) when your data is a sample drawn from a larger group, which is the usual case for surveys. Use the population version (dividing by n) only when your data covers the entire group.
When should you use it?
Use this calculator whenever you have a list of numbers and you want to know how consistent or how varied they are. It works well for test scores, prices, wait times, survey ratings, daily sales, ages, or any measurement collected from a group. The average on its own only tells you the middle value. Standard deviation goes further and tells you whether most values sit close to that middle or are spread far apart. Reach for it any time the question "how much do these vary?" matters as much as the average itself.
What does the result mean?
The result is a single number in the same units as your data. A small standard deviation means your numbers are tightly grouped near the average, so things are consistent. A large one means they are widely scattered. There is no fixed "good" value, because it depends on your scale; a spread of 2 is small for exam marks out of 100 but large for shoe sizes. For roughly bell-shaped data, a widely used guideline is that about two thirds of the values fall within one standard deviation of the average.
Mistakes to avoid
Do not mix different things in one list; keep it to one type of measurement, such as all test scores or all prices. Enter every value, not just the highest and lowest, or the answer will be wrong. Watch for typos, because one stray large number can badly inflate the spread. Do not confuse standard deviation with the average, as they answer different questions. Finally, check that you have not accidentally entered a number twice or left a blank, since both of these will change the result.
How to use this calculator
- Type or paste your numbers into the box, separating each one with a comma, a space, or a new line.
- Check that every value is a plain number and that none are missing or entered twice by mistake.
- If the calculator offers a choice, pick "sample" for survey data or "population" when your numbers are the entire group.
- Read the standard deviation result: a small number means your values are consistent, a large one means they are spread out.
Worked example
Imagine five customers rate your service out of 10 and give 6, 7, 8, 9, and 10. The average is 8. When you enter those five scores, the calculator returns a standard deviation of about 1.6. That means most ratings landed within roughly 1.6 points of the average, so opinions were fairly close together rather than wildly split.
Frequently asked questions
What does standard deviation tell me?
It measures spread. A small standard deviation means responses cluster near the mean; a large one means they are widely dispersed.
What do I type in the box?
Type the numbers you want to measure, one after another. Separate each number with a comma, a space, or a new line, and use plain numbers with no words or symbols.
Where do I get these numbers from?
They come from whatever you are measuring, such as test marks, survey answers, prices, times, or counts. If your results are already in a spreadsheet, you can copy the column and paste it straight in.
What does the final number actually tell me?
It tells you how far your values typically sit from the average. A smaller number means they are close together and consistent, while a larger number means they are more spread out.
What is the difference between sample and population standard deviation?
Population is used when your numbers are the whole group. Sample is used when they are only a portion you are using to estimate a bigger group. For most surveys the sample version is the right choice, and it gives a slightly larger number.
Is standard deviation the same as the average?
No. The average is the middle value of your numbers. The standard deviation tells you how spread out they are around that middle, so you usually look at both together.
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