# Slope Calculator

If you were searching for how to find a slope with two points of a line, this **slope calculator** is what you need.

Calculating slope and its formula is the first step to understanding more complex topics in math or physics:

- The slope concept is necessary to understand the
**derivative**of a function. - Once you understand the derivative concept, you'll notice that
**velocity**is no more than the derivative of position with respect to time. - If you're studying solid mechanics, you'll figure out that the slope of the linear portion of the stress-strain diagram equals the famous
**Young's modulus**. - When studying the normal force over objects lying on inclined surfaces, you'll find out that this normal force varies with the slope of that surface.

This tool also has **other functionalities**:

- Calculating the
**y-intercept**of the line forming those two points. - Calculating the
**distance**between the two points. - Calculating the
**slope percentage**and calculating the slope**angle**.

Read on to learn more about the slope equation used to calculate slope with two points and how to calculate those other terms.

## Slope formula

If you have two points (`x₁, y₁`

, and `x₂, y₂`

) and want to calculate the slope, the equation to use is:

`m = (y₂ - y₁)/(x₂ - x₁)`

where:

`m`

— Slope of the line;`x₁`

— x coordinate of the first point;`y₁`

— y coordinate of the first point;`x₂`

— x coordinate of the second point; and`y₂`

— y coordinate of the second point.

## How to find a slope with two points

- Identify the two points:
`(x₁, y₁)`

and`(x₂, y₂)`

. - Subtract the
`y`

coordinate of the second point to the y coordinate of the first point:`y₂ - y₁`

. - Subtract the
`x`

coordinate of the second point to the x coordinate of the first point:`x₂ - x₁`

. - Finally, to calculate the slope m by dividing the subtraction of the
`y`

coordinates by the subtraction of the`x`

coordinates:`m = (y₂ - y₁)/(x₂ - x₁)`

(this is the slope formula)

## Angle and percent grade: slope-related measurements

This tool also calculates the **slope angle**, the angle the line forms about the horizontal axis. To find this angle (`θ`

), just calculate the inverse tangent (`arctan`

) of the slope `m`

`θ = arctan(m)`

💡 Key points:

- For
**positive**slopes, the angle is positive and measured about the right part of the x-axis. - For
**negative**slopes, the angle is**negative**and measured about the left part of the x-axis. - A higher absolute value of slope (
`m`

) implies a higher absolute value for the angle (`θ`

).

**Percent grade** or **slope percentage** is simply the slope expressed as a percentage. For example, for `m = 1`

, the percent grade equals `100%`

, while an `m = 0.5`

implies a `50%`

percent grade. **To calculate the slope percentage, multiply the slope by 100**.

## Calculating the y-intercept

The y-intercept is **the point where the function intersects the y-axis**, and we can calculate it with one of the following formulas:

`b = y₂ - mx₂`

`b = y₁ - mx₁`

As we can see, to calculate the y-intercept, we only need one point (`x₁, y₁`

or `x₂, y₂`

) and the slope.

## Calculating the distance between two points

To calculate the distance between two points (`d`

), we use the following formula, which relies on the Pythagorean theorem:

`d = √[(x₂ - x₁)² + (y₂ - y₁)²]`