Standard Deviation Calculator

StatisticsLast updated: August 17, 2026

Standard deviation is the most widely used measure of how far a set of values spreads out around its mean. A small standard deviation means the values cluster tightly around the mean; a large one means they are spread across a wide range.

This calculator returns both the sample standard deviation (with the n−1 denominator, the one used in research) and the population standard deviation (with the n denominator). It also reports variance, mean, median, quartiles, the coefficient of variation, and the rest of the descriptive statistics.

Both decimal points and decimal commas are accepted (e.g. 3.14 or 3,14). At least 2 values are required.

Formula

Sample:     s = √( Σ(xᵢ − x̄)² / (n − 1) )
Population: σ = √( Σ(xᵢ − μ)² / n )
Variance = the square of the standard deviation (s² or σ²)

If your data is a sample (as research data usually is), use the formula with the n−1 denominator; it gives an unbiased estimate of the population standard deviation (Bessel's correction).

How to Calculate

  1. Paste your data values into the box — separate them with commas, spaces, or line breaks.
  2. Choose whether your data is a sample (n−1) or the entire population (n).
  3. Read the standard deviation, variance, and full descriptive statistics in the results section.
  4. The interpretation line explains the mean ± 1 standard deviation range in plain English.

Worked Examples

Spread of exam scores

For five students scoring 70, 75, 80, 85, and 90, the mean is 80.00, the sample variance is 62.5000, and the sample standard deviation is 7.9057. Scores deviate from the mean by roughly 8 points.

Sample standard deviation (s): 7.9057 · Sample variance (s²): 62.5000 · Mean (x̄): 80.0000

Production measurements (population)

When every value is identical (10, 10, 10, 10) there is no spread at all: the standard deviation is 0 and the variance is 0.

Population standard deviation (σ): 0.0000 · Population variance (σ²): 0.0000 · Mean (x̄): 10.0000

Data written with decimal commas

Decimal commas are accepted: for the data 2,5 3,1 2,8 3,4 2,9 3,0 the mean is 2.9500 and the sample standard deviation is 0.3017.

Sample standard deviation (s): 0.3017 · Sample variance (s²): 0.0910 · Mean (x̄): 2.9500

Frequently Asked Questions

What is the difference between sample and population standard deviation?
The population standard deviation (σ) is used when you have measured the entire population, and the sum of squares is divided by n. The sample standard deviation (s) is used when you are working with a sample drawn from a population, and the sum of squares is divided by n−1 (Bessel's correction). For research data, the sample formula is almost always the correct choice.
What does the standard deviation actually tell you?
It tells you how far the values sit from the mean on average. In a normal distribution, about 68% of values fall within one standard deviation of the mean and about 95% fall within two.
How are standard deviation and variance related?
Variance is the average of the squared deviations; the standard deviation is the square root of the variance. The standard deviation is easier to interpret because it is expressed in the same unit as the data itself.
Can the standard deviation be zero?
Yes — if every value is identical, the spread is zero. It can never be negative: because it is a square root, it is always 0 or positive.
What is the coefficient of variation (CV)?
It is the standard deviation expressed as a percentage of the mean. It lets you compare the variability of data sets measured in different units or on different scales; a series with a CV of 10% is more homogeneous than one with a CV of 25%.
Does it give the same result as SPSS?
Yes. SPSS, Excel (STDEV.S), and R all compute the sample standard deviation (n−1) by default, so with 'Sample' selected the results match exactly.