Excel Standard Deviation Formula Calculator

Calculate standard deviation using Excel’s STDEV.S and STDEV.P formulas.

Chart of Data Points and Mean

What is the formula Excel uses to calculate standard deviation?

Standard deviation is a crucial statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. In Microsoft Excel, there isn’t just one formula, but two primary functions to calculate standard deviation, and the one you use depends on your data.

• STDEV.S: This function calculates the standard deviation based on a sample of a population. It uses the “n-1” method. This is the most common scenario, as we often analyze a subset of data to infer conclusions about the whole.
• STDEV.P: This function calculates the standard deviation for an entire population. It uses the “n” method. You should only use this if you are certain that your data includes every single member of the group you are studying.

Standard Deviation Formula and Explanation

The core difference between the sample and population formulas lies in the denominator. Both start by calculating the mean (average) of the data set and then finding the squared difference of each data point from that mean.

Formula for Sample Standard Deviation (STDEV.S)

This is the formula Excel uses for its STDEV.S function:

s = √[ Σ(x_i – x̄)² / (n – 1) ]

Formula for Population Standard Deviation (STDEV.P)

This is the formula Excel uses for its STDEV.P function:

σ = √[ Σ(x_i – μ)² / N ]

Formula Variables

Variable	Meaning	Unit	Typical Range
s or σ	Standard Deviation	Same as input data	Non-negative number (0 or greater)
Σ	Summation	N/A	N/A
xi	Each individual data point	Same as input data	Varies
x̄ or μ	The mean (average) of the data points	Same as input data	Varies
n or N	The number of data points (count)	Unitless	Positive integer

The use of (n-1) in the sample formula is known as Bessel’s correction, which provides a more accurate estimate of the population standard deviation when you’re only working with a sample.

Practical Examples

Example 1: Calculating Sample Standard Deviation

Imagine a teacher wants to understand the variability in test scores for a class of 10 students. The scores are: 85, 92, 78, 88, 95, 81, 79, 89, 90, 83. Since this is just one class (a sample of all students), we use STDEV.S.

• Inputs: 85, 92, 78, 88, 95, 81, 79, 89, 90, 83
• Mean (Average): 86
• Sum of Squared Differences: 310
• Calculation: √[ 310 / (10 – 1) ] = √[34.44] ≈ 5.87
• Result (STDEV.S): Approximately 5.87

You can verify this calculation using our Variance Calculator.

Example 2: Calculating Population Standard Deviation

Now, let’s say a small company has only 5 employees, and we want to calculate the standard deviation of their ages. The ages are: 25, 30, 35, 40, 45. Since we have data for every employee, this is the entire population.

• Inputs: 25, 30, 35, 40, 45
• Mean (Average): 35
• Sum of Squared Differences: 250
• Calculation: √[ 250 / 5 ] = √ ≈ 7.07
• Result (STDEV.P): Approximately 7.07

How to Use This formula excel uses to calculate standard deviation Calculator

1. Enter Your Data: Type or paste your numerical data into the “Data Points” text area. The numbers can be separated by commas, spaces, or on new lines.
2. Select the Type: Choose between “Sample (STDEV.S)” and “Population (STDEV.P)”. If you’re unsure, “Sample” is the most common and safer choice.
3. Calculate: Click the “Calculate” button.
4. Interpret Results: The calculator will display the final standard deviation, along with intermediate values like the mean, variance, and count of your data points. The chart provides a visual representation of your data’s distribution.

Key Factors That Affect Standard Deviation

• Outliers: Extreme values, or outliers, can significantly increase the standard deviation, as the squaring process gives them more weight.
• Sample Size (n): For a sample standard deviation, a smaller sample size (n) will lead to a larger result because you are dividing by a smaller number (n-1).
• Data Spread: The more spread out the data points are from the mean, the higher the standard deviation will be. Data clustered tightly around the mean results in a low standard deviation.
• Data Distribution: While not a direct input, the shape of the data’s distribution (e.g., normal, skewed) affects the interpretation of the standard deviation. For a normal distribution, about 68% of data lies within one standard deviation of the mean.
• Measurement Scale: The standard deviation is expressed in the same units as the original data. Changing the scale (e.g., from feet to inches) will change the standard deviation.
• Adding a Constant: If you add the same constant value to every data point, the standard deviation does not change because the spread of the data remains the same.

For more advanced analysis, explore our Statistical Significance Calculator.

FAQ about the formula excel uses to calculate standard deviation

What’s the main difference between STDEV.S and STDEV.P?

STDEV.S is for a sample of data, while STDEV.P is for an entire population. STDEV.S divides the sum of squared differences by (n-1), whereas STDEV.P divides by n.

When should I use STDEV.S?

You should use STDEV.S almost all the time. It’s rare to have data for an entire population. Use it when you are analyzing a subset of data to make generalizations about a larger group.

Can the standard deviation be negative?

No. Since the formula involves squaring differences (which always results in a positive number) and then taking the square root, the standard deviation can only be zero or positive.

What does a standard deviation of 0 mean?

A standard deviation of 0 means there is no variability in the data; all the data points are identical.

Is a high standard deviation good or bad?

It’s neither inherently good nor bad; it depends on the context. In manufacturing, a low standard deviation is desired for consistency. In investing, a high standard deviation means higher risk but also potentially higher returns.

Why does Excel have older functions like STDEV and STDEVP?

These are older functions kept for backward compatibility with older versions of Excel. STDEV is equivalent to STDEV.S, and STDEVP is equivalent to STDEV.P. Microsoft recommends using the newer .S and .P functions.

How does standard deviation relate to variance?

The standard deviation is simply the square root of the variance. Variance is measured in squared units, while standard deviation is in the original units of the data, making it often easier to interpret.

Does this calculator handle non-numeric text?

Yes, just like Excel’s STDEV.S and STDEV.P functions, our calculator will parse the numbers from your input and ignore any text, empty spaces, or non-numeric characters.

Interested in other Excel formulas? Check out our Excel Formulas Guide.

Related Tools and Internal Resources

• {related_keywords} – Calculate the average of a dataset.
• {related_keywords} – Find the variance for both sample and population data.
• {related_keywords} – Understand how many standard deviations a data point is from the mean.
• {related_keywords} – Explore the properties of the bell curve.