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Standard Deviation Calculator

Use this free online standard deviation calculator to find the standard deviation and variance of any dataset. Enter your numbers to measure how spread out your data is.

Standard Deviation

Add numbers to measure data spread

Add at least one number to see results.

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Formula

SD = sqrt(Sum((xi - mean)^2) / N)

Find the mean, calculate the squared difference of each value from the mean, average those squared differences, and take the square root.

Worked Example

Dataset: 2, 4, 4, 4, 5, 5, 7, 9 Step 1: Mean = 40/8 = 5 Step 2: Squared differences: 9, 1, 1, 1, 0, 0, 4, 16 Step 3: Variance = 32/8 = 4 Step 4: SD = sqrt(4) = 2 Result: Standard Deviation = 2

What Is Standard Deviation?

Standard deviation is a measure of how spread out the values in a dataset are from the mean. A low standard deviation means data points are clustered close to the mean, while a high standard deviation means data is spread over a wider range of values.

A standard deviation of 0 means all values are identical
About 68% of data falls within one standard deviation of the mean (in normal distributions)
About 95% falls within two standard deviations, and 99.7% within three (the 68-95-99.7 rule)
Variance is the square of the standard deviation and is useful for statistical calculations

Standard deviation is essential in finance (measuring investment risk), quality control (manufacturing tolerances), science (experimental precision), education (grading curves), and any field that needs to quantify variability or consistency.

You can also calculate changes using our Average Calculator or Mean Median Mode Calculator.

Frequently Asked Questions

What does standard deviation tell you?

It measures the spread or dispersion of data points from the mean. A low SD means data is clustered near the mean (consistent). A high SD means data is spread out (variable).

What is the difference between population and sample SD?

Population SD divides by N (the total count). Sample SD divides by N-1 (Bessel's correction) to provide an unbiased estimate of the population SD when working with a sample.

What is variance?

Variance is the square of the standard deviation. It represents the average of the squared differences from the mean. While harder to interpret directly (since its units are squared), it is useful in many statistical formulas.

What is the 68-95-99.7 rule?

In a normal (bell-shaped) distribution, approximately 68% of values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. This is also called the empirical rule.

How is standard deviation used in finance?

In finance, standard deviation measures investment volatility (risk). A stock with a high SD has unpredictable returns. Portfolio managers use SD to balance risk and return across investments.

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