Standard Deviation Calculator

1. 01Enter your numbersType each value into its own row. Use "Add number" for more rows.
2. 02Read the resultsThe population standard deviation, sample standard deviation, variance, and mean update automatically as you type.

• Statistics homework and examsCheck a hand-calculated standard deviation, or quickly work through a dataset without redoing the arithmetic by hand.
• Analyzing test scores or measurementsSee how spread out a set of scores or measurements is around the mean — a low standard deviation means values cluster tightly, a high one means they vary widely.
• Quality control and consistency checksMeasure the consistency of repeated measurements (for example, product weights or timing results) by comparing their standard deviation.

• A classic datasetFor 2, 4, 4, 4, 5, 5, 7, 9: the mean is 5, and the population standard deviation is exactly 2.
• Identical valuesFor 4, 4, 4, 4: the standard deviation is 0, since there is no spread at all.
• A small sampleFor 1, 2, 3, 4, 5: the sample standard deviation (≈1.58) is slightly larger than the population standard deviation (≈1.41), because the sample formula corrects for the bias of estimating from a subset.

Standard deviation measures how spread out a set of numbers is around the mean. First, the mean is subtracted from each value and the result squared; these squared differences are averaged to get the variance, and the square root of the variance is the standard deviation. Population standard deviation divides by the count (n). Sample standard deviation divides by (n − 1) instead, known as Bessel's correction, which corrects for the tendency of a sample to underestimate the true population spread.

Use population standard deviation when your numbers represent the entire group you care about (for example, every student in a specific class). Use sample standard deviation when your numbers are a subset used to estimate a larger, unknown population (for example, a survey of 50 customers used to estimate all customers). When in doubt, most statistics courses and tools default to the sample version.

Enter any list of numbers, including negative numbers and decimals. The tool returns the count, mean, population variance and standard deviation, and sample variance and standard deviation. Sample statistics require at least 2 values, since dividing by (n − 1) is undefined for a single value.

The calculation runs entirely in your browser. The numbers you enter are never uploaded, stored, or shared, and closing the tab clears everything.

What is the difference between population and sample standard deviation?

Population standard deviation treats your numbers as the complete dataset and divides by the count (n). Sample standard deviation treats your numbers as a sample drawn from a larger population and divides by (n − 1), which slightly increases the result to correct for sampling bias.

Why do I need at least 2 numbers for sample standard deviation?

The sample formula divides by (n − 1). With only one value, that becomes division by zero, so sample standard deviation is undefined for a single data point.

What does a standard deviation of 0 mean?

It means every value in your list is identical — there is no variation at all.

What is variance?

Variance is the standard deviation squared. It measures the same spread as standard deviation, but in squared units, which makes standard deviation easier to interpret directly against the original data.

Is my data saved?

No. Everything is calculated in your browser; nothing is sent to a server.