## Summary

The Excel SLOPE function returns the slope of a regression line based on known y values and known x values. A regression line is a "best fit" line based on known data points.

## Purpose

Get slope of linear regression line

## Return value

Calculated slope as a number

## Syntax

``=SLOPE(known_ys,known_xs)``
• known_ys - An array or range of numeric data points (dependent values).
• known_xs - An array or range of numeric data points (independent values).

## How to use

The SLOPE function returns the slope of a regression line based on known y values and known x values. A regression line is a "best fit" line based on known data points.

The slope of a line is a measure of steepness. Mathematically, slope is calculated as "rise over run", or change in y over the change in x. For example, if a line has a slope of 2/1 (2), then if y increases by 2 units, x increases by 1 unit.

### Example

In the example shown, the formula in E5 is:

``````=SLOPE(B5:B9,C5:C9) // returns -2
``````

This formula returns -2, based on known_ys in C5:C9, and known_xs in B5:B9.

### Equation

In statistics, a best fit line does not normally lie exactly on the known x and y points. The equation used by the SLOPE function in Excel is based on the mean of known x's and y's:

For the example shown, this formula can be manually recreated like this:

``````=SUM((B5:B9-AVERAGE(B5:B9))*(C5:C9-AVERAGE(C5:C9)))/SUM((B5:B9-AVERAGE(B5:B9))^2)
``````

The calculated result from the SLOPE function and the manual formula are the same.

### Notes

• If there is only one set of points, SLOPE will return #DIV/0!
• If the count of known_ys is different from known_xs, SLOPE returns #N/A

Author

### Dave Bruns

Hi - I'm Dave Bruns, and I run Exceljet with my wife, Lisa. Our goal is to help you work faster in Excel. We create short videos, and clear examples of formulas, functions, pivot tables, conditional formatting, and charts.