Slope and Gradient Calculator

This calculator provides varies methods to compute the slope (also known as gradient). The methods are the slope-intercept form, point-slope form, slope of a right-angle triangle, and the Euler line form. 
CalculationVarious methods for calculating the slope/gradient are provided in the toggles below.
1) Slope-intercept form
2) Point-slope form
3) Slope of a right-angle triangle
4) Euler line form
Inputs﻿﻿m1
:4.00​
﻿
﻿﻿m2
:5.00​
﻿
﻿﻿m3
:8.00​
﻿
Output﻿﻿m,E
:-0.19​
﻿
﻿
The Euler Line is a line determined from any triangle that is not equilateral. The line passes through the centroid (the center of mass), the orthocenter (where the altitudes meet) and the circumcenter (the center of the circumscribed circle) of a triangle. The Euler line is given by:
﻿
mE =−[m1 m2 + m1 m3 + m2 m3 + 3m1 + m2 + m3 + 3  m1 m2 m3]m_{E}\ = -\left[\dfrac{m_{1} \ m_{2}\ +\ m_{1} \ m_{3}\ +\ m_{2} \ m_{3}\ +\ 3}{m_{1}\ +\ m_{2}\ +\ m_{3}\ +\ 3\ \ m_{1} \ m_{2}\ m_{3}}\right]mE​ =−[m1​ + m2​ + m3​ + 3  m1​ m2​ m3​m1​ m2​ + m1​ m3​ + m2​ m3​ + 3​]
Where:
﻿﻿m1​,m2​
 and ﻿m3​
 are the slopes of each of the three sides of the triangle 
﻿﻿mE​
 is the resulting slope of the Euler line 
﻿
Euler line form
ExplanationSlope and gradient are dimensionless measures of the steepness of a line. They are calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, this is given by:
﻿
m=riserun=Δ verticalΔ horizontalm=\dfrac{\text{rise}}{\text{run}}=\dfrac{\Delta \text{ vertical}}{\Delta \text{ horizontal}}m=runrise​=Δ horizontalΔ vertical​
The terms slope and gradient are often used interchangeably, though gradient is sometimes distinguished from slope as being a vector quantity (while slope is a scalar).  
The importance of slope and gradient is vast and spans multiple fields:
Physics, in a distance-time graph the slope gives the velocity, and in a velocity-time graph the slope provides the acceleration.
Geography and civil engineering, the slope of land influences the rate of surface runoff, soil erosion and determines the design of certain structures like roads and buildings.
Economics and business, the slope of a supply or demand curve gives the rate of change of quantity supplied or demanded with respect to price.
In summary, slope and gradient are fundamental concepts in mathematics and science, providing a measure of change and playing a crucial role in understanding and interpreting phenomena in various fields.
Related ResourcesEquilateral Triangle Calculator 
Heron's Formula Calculator 
Pythagorean Theorem Calculator
Tangential Angle Method for setting out circular curves 
Check out our full library of CalcTree templates here!
﻿
﻿