Slope Calculator

Created by Luis Hoyos
Last updated: Jul 05, 2022
Table of contents:

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

1. Identify the two points: (x₁, y₁) and (x₂, y₂).
2. Subtract the y coordinate of the second point to the y coordinate of the first point: y₂ - y₁.
3. Subtract the x coordinate of the second point to the x coordinate of the first point: x₂ - x₁.
4. 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)

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]

Luis Hoyos
First point coordinates
x₁
y₁
Second point coordinates
x₂
y₂
Result
Slope (m)
Related numbers
Y - intercept
Angle (θ)
deg
Percentage grade
%
Distance (d)
Distance between x's (Δx)
Distance between y's (Δy)
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