Slope Calculator

Calculate slope, line equation, angle, and distance from two points (x1, y1) and (x2, y2).

Enter Two Points

Point 1 (x1, y1)
Point 2 (x2, y2)

Result

Slope (m)
--
rise / run
Slope (m)--
Slope as Fraction--
Angle of Inclination--
Rise (Δy)--
Run (Δx)--
Distance--
Midpoint--
Slope-Intercept Form--
Point-Slope Form--
Perpendicular Slope--

Step-by-Step Solution

Understanding Slope

Slope measures the steepness and direction of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A positive slope means the line goes upward from left to right, while a negative slope means it goes downward.

Slope Formulas

Slope Formula

The slope between two points (x1, y1) and (x2, y2).

m = (y2 - y1) / (x2 - x1)

Slope-Intercept Form

Standard form of a linear equation where m is slope and b is y-intercept.

y = mx + b

Point-Slope Form

Equation of a line through point (x1, y1) with slope m.

y - y1 = m(x - x1)

Distance Formula

The distance between two points in a plane.

d = sqrt((x2-x1)^2 + (y2-y1)^2)

Angle of Inclination

The angle the line makes with the positive x-axis.

θ = arctan(m)

Perpendicular Slope

The slope of a line perpendicular to a line with slope m.

m_perp = -1/m

Types of Slope

  • Positive slope: Line rises from left to right (m > 0).
  • Negative slope: Line falls from left to right (m < 0).
  • Zero slope: Horizontal line (m = 0).
  • Undefined slope: Vertical line (division by zero).

Applications

Slope is used in construction (roof pitch), road engineering (grade), economics (rate of change), physics (velocity), and data analysis (trend lines). Understanding slope is fundamental to calculus, where the derivative represents the slope of a curve at any point.