Standard Deviation Calculator
Enter your numbers to see the mean, variance, and standard deviation.
Paste a list of numbers and instantly see the mean, variance, and standard deviation. This calculator gives you both the population result (divided by n) and the sample result (divided by n minus 1), so you can pick the one that fits your data. Everything runs in your browser, with nothing sent to a server.
How to use
- Type or paste your numbers into the box. Separate them with commas, spaces, or new lines.
- Read the count, sum, and mean of your data set as you type.
- Compare the population standard deviation (for a full data set) with the sample standard deviation (for a subset).
- Use the Copy button next to any result to grab the exact value.
- Press Reset to clear the box and start over.
Examples
- Input: 2, 4, 4, 4, 5, 5, 7, 9. Mean 5, population standard deviation 2, sample standard deviation about 2.138.
- Input: 10 20 30 40 50. Mean 30, population variance 200, sample variance 250.
- Input of a single value like 42 returns the mean and a population standard deviation of 0, while the sample result needs at least two values.
FAQs
- What is the difference between population and sample standard deviation?
- Use the population formula when your numbers cover the entire group you care about. Use the sample formula when your numbers are a subset drawn from a larger group. The sample formula divides by n minus 1 instead of n, which gives a slightly larger value to correct for the smaller data set.
- Why does the sample result need at least two values?
- The sample formula divides by n minus 1. With only one value that would mean dividing by zero, which is undefined, so the calculator shows population statistics only and notes that the sample result needs at least two values.
- How should I separate my numbers?
- You can use commas, spaces, tabs, or new lines, or any mix of them. Pasting a column from a spreadsheet works because each value sits on its own line.
- Does it handle negative numbers and decimals?
- Yes. Negative values and decimals are fully supported. Any token that is not a valid number is flagged so you can fix it.
- How are the results rounded?
- Results are shown to about eight significant digits to avoid floating point noise while staying precise. The underlying calculation uses full precision, and the Copy button copies the full value.
- Is my data sent anywhere?
- No. The calculation runs entirely in your browser. Your numbers never leave your device.
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