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Standard Deviation Calculator

Calculate standard deviation, variance, mean, sum, count, and more for any dataset. Supports both sample and population formulas. Free, private, and runs entirely in your browser.

Enter Your Data

Paste or type your numbers. The calculator accepts newlines, commas, spaces, and tabs as separators.
Use Sample when your data is a subset of a larger population. Use Population when you have data for every member of the group.

Enter your dataset and click Calculate to see standard deviation and other statistics here.

What does this standard deviation calculator do?

This free online standard deviation calculator computes the standard deviation, variance, mean, sum, count, and other key statistics for any dataset. It supports both the sample standard deviation formula (using n−1 in the denominator) and the population standard deviation formula (using N).

Standard deviation is one of the most important measures in statistics. It tells you how spread out your data is around the mean. A low standard deviation means values are clustered close to the average, while a high standard deviation means values are spread over a wider range. Whether you're analysing test scores, stock returns, scientific measurements, or survey data, this calculator gives you accurate results instantly — with the formula shown so you can follow the math.

How to use the standard deviation calculator

  1. Enter your data: Type or paste your numbers into the text area. One number per line works best, but commas, spaces, and tabs are also accepted.
  2. Choose sample or population: Select Sample (n−1) if your data is a subset of a larger group. Select Population (N) if your data includes every member of the group.
  3. Click Calculate: The result appears instantly along with mean, variance, sum, count, median, and range.
  4. Read the results: Standard deviation and variance are shown prominently, with additional statistics in the grid below.

Use the Example button to load a sample dataset and see how the calculator works.

Why use this standard deviation calculator?

100% private

Everything runs in your browser. The numbers you enter never leave your device — no server, no logs, no tracking.

Sample & population

Switch between sample (n−1) and population (N) formulas with a single click.

Complete statistics

Get standard deviation, variance, mean, sum, count, median, range, and sum of squares all at once.

Formula shown

Each result includes the formula used, so you can learn the method as you calculate.

Clear error messages

Too few data points for sample standard deviation or invalid input is explained clearly.

Works offline

Once the page loads, you can perform standard deviation calculations without an internet connection.

Standard deviation formulas explained

Population standard deviation

When your dataset includes every member of the group you're studying, use the population standard deviation formula:

σ = √( Σ(xᵢ − μ)² / N )

Where σ is the population standard deviation, xᵢ are the individual values, μ is the population mean, and N is the total number of values. The population variance is σ².

Sample standard deviation

When your data is a subset (sample) drawn from a larger population, use the sample standard deviation formula with n−1 in the denominator:

s = √( Σ(xᵢ − x̄)² / (n − 1) )

Where s is the sample standard deviation, x̄ is the sample mean, and n is the number of values in the sample. Dividing by n−1 instead of n is called Bessel's correction, and it makes the sample standard deviation an unbiased estimator of the population standard deviation.

Variance

Variance is the average of the squared differences from the mean. It is the square of the standard deviation. The population variance is σ², and the sample variance is s². Variance is expressed in squared units, while standard deviation is expressed in the same units as the original data — which makes standard deviation easier to interpret.

Mean (average)

The mean is the sum of all values divided by the count: x̄ = Σxᵢ / n. It is the centre point around which standard deviation is measured.

Sum of squares

The sum of squares (SS) is Σ(xᵢ − mean)². It measures the total squared deviation from the mean and is the numerator in both variance formulas before division.

Worked example

Suppose you have the dataset: 2, 4, 4, 4, 5, 5, 7, 9. Here is how the calculations work out:

  • Count (n or N): 8
  • Mean: (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) ÷ 8 = 40 ÷ 8 = 5
  • Sum of squares: (2−5)² + (4−5)² + (4−5)² + (4−5)² + (5−5)² + (5−5)² + (7−5)² + (9−5)² = 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32
  • Population variance (σ²): 32 ÷ 8 = 4
  • Population standard deviation (σ): √4 = 2
  • Sample variance (s²): 32 ÷ 7 ≈ 4.5714
  • Sample standard deviation (s): √4.5714 ≈ 2.1381

Notice how the sample standard deviation is slightly larger than the population standard deviation because we divide by n−1 (7) instead of n (8).

Where standard deviation is used

  • Education: Analysing test scores and grading on a curve.
  • Finance: Measuring volatility of stock returns and investment risk.
  • Science: Reporting measurement uncertainty and experimental error.
  • Quality control: Monitoring manufacturing consistency and process variation.
  • Sports: Evaluating player consistency and performance variability.
  • Healthcare: Assessing variability in patient metrics like blood pressure or cholesterol.
  • Psychology: Interpreting standardised test scores and research data.

Frequently asked questions

Yes, completely free. No signup, no watermark, no hidden charges. Perform as many standard deviation calculations as you want.
Population standard deviation (σ) uses N in the denominator and is used when you have data for every member of a group. Sample standard deviation (s) uses n−1 in the denominator and is used when your data is a subset of a larger population. The n−1 correction (Bessel's correction) makes the sample standard deviation an unbiased estimator of the population standard deviation.
Absolutely. Everything runs in your browser using JavaScript. The numbers you enter never leave your device — there is no server processing, no logging, and no data storage.
Variance is the average of the squared differences from the mean. It is the square of the standard deviation. Variance is expressed in squared units, while standard deviation is expressed in the same units as the original data.
Use population standard deviation when your dataset includes every member of the group you're studying (for example, all students in a class). Use sample standard deviation when your data is a subset of a larger population (for example, a random sample of voters in a country).
No. Standard deviation is always zero or positive because it is the square root of variance, which is always non-negative. A standard deviation of zero means all values in the dataset are identical.
Paste or type your numbers into the text area, one per line or separated by commas, spaces, or tabs. The calculator automatically parses them.
The sample standard deviation formula divides by n−1. If n = 1, you'd be dividing by zero, which is undefined. With only one data point, you cannot estimate variability. Population standard deviation technically works with 1 value (result is 0), but it's not meaningful either.