What is a standard deviation calculator?

A standard deviation calculator is a free statistics tool that measures the spread of a data set around its mean. Our standard deviation calculator supports both sample (n-1) and population (n) standard deviation, and shows the variance, mean, min, max, and range. The standard deviation calculator is used in finance, science, quality control, and grading.

What is standard deviation in simple terms?

Standard deviation measures how spread out your data is from the mean (average). A low standard deviation means data points cluster close to the average. A high standard deviation means they are spread widely.

What is a good standard deviation?

It depends on context. For investment returns, a 15-20% annual standard deviation is typical for a diversified stock portfolio. For test scores, a standard deviation of 10-15 is common. Compare to other data in the same domain rather than an absolute threshold.

How do I calculate standard deviation in Excel?

Use =STDEV() for sample standard deviation or =STDEVP() for population standard deviation. Type your data in a column, then enter the formula in an empty cell. Excel handles the rest. Google Sheets has the same functions.

What is the difference between variance and standard deviation?

Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance. They convey the same information, but standard deviation is in the original units (more interpretable), while variance is in squared units.

Standard Deviation Calculator - Calculate Variance & Mean

Enter your data set

Type your numbers separated by commas or newlines. The calculator accepts any size data set from a few points to thousands.

Choose sample or population

Select Sample (when your data is a subset of a larger population) or Population (when you have all values). The formulas differ slightly.

See the full statistics

Get the mean, variance, standard deviation, range, and a histogram. Standard deviation tells you the typical spread of values from the mean.

Key things to know about our standard deviation calculator:

68-95-99.7 rule: For a normal distribution, 68% of values fall within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. Useful for quality control and grading curves.
Sample vs population: Use Sample (divide by n-1) when generalizing to a larger population. Use Population (divide by n) when you have all values.
Use cases: Investment volatility, test score spread, manufacturing tolerances, scientific data analysis, and grade normalization are common uses.

For related calculations, try our percentage calculator.

Standard Deviation Calculator

Standard Deviation Calculator

Sample vs. Population Standard Deviation

Sample Standard Deviation

Population Standard Deviation

How our standard deviation calculator works

Enter your data set

Choose sample or population

See the full statistics

Key things to know about our standard deviation calculator:

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