Find the standard deviation of any data set. This free calculator gives the sample and population standard deviation, variance, mean, count and range — just paste your numbers.
Your data
Use sample when your numbers are a subset of a larger group (divides by n−1); use population when they’re the entire group (divides by n).
Standard deviation (sample)
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Enter some numbers
Mean
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Variance
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Count
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Sum
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Min / Max
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Other SD
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Standard deviation measures how spread out your numbers are around the mean. A larger value means more spread. The calculator also shows variance (the square of the standard deviation).
Use this free standard deviation calculator to find the standard deviation of a set of numbers. Paste your data, choose sample or population, and get the standard deviation, variance, mean and more.
What this standard deviation calculator shows you
A standard deviation calculator measures how spread out your numbers are around their average. It returns both the standard deviation and variance, plus the mean, count, sum and range — for either a sample or a whole population.
How standard deviation is calculated
1. Find the mean
2. Square each value's distance from the mean, and sum
3. Divide by n (population) or n − 1 (sample)
4. Standard deviation = square root of that
For the data 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, the population standard deviation is 2, and the variance is 4.
Sample vs population standard deviation
Use
When
Divides by
Sample (s)
Your data is part of a larger group
n − 1
Population (σ)
Your data is the entire group
n
Sample standard deviation is slightly larger because dividing by n − 1 corrects for estimating from a subset (Bessel’s correction).
What does standard deviation tell you?
A small standard deviation means the values cluster tightly around the mean; a large one means they’re more spread out. It’s widely used in statistics, finance (volatility), science and quality control.
How to use the standard deviation calculator
Paste your numbers, separated by commas, spaces or new lines.
Choose sample or population.
Read the standard deviation, variance and summary stats.
Standard Deviation FAQ
How do I calculate standard deviation?
Find the mean, sum the squared differences from the mean, divide by n (population) or n−1 (sample), then take the square root. This calculator does it instantly.
What's the difference between sample and population?
Use population when your numbers are the entire group (divide by n), and sample when they're a subset of a bigger group (divide by n−1). Sample SD is slightly larger.
What is variance?
Variance is the average squared distance from the mean — the square of the standard deviation. This tool shows both.
What does a high standard deviation mean?
It means the values are spread widely around the mean. A low standard deviation means they're clustered close to the average.
How do I enter my data?
Paste or type your numbers separated by commas, spaces or new lines. The calculator ignores anything that isn't a number.
Is the standard deviation calculator free?
Yes, this standard deviation calculator is completely free, needs no sign-up, and gives instant results in your browser.
