Slope Calculator

Calculate line slope (m), angle, percent grade, distance, midpoint, perpendicular slope, and convert between Slope-Intercept, Point-Slope, and Standard forms.

Slope Parameters

Quick Presets
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Calculated Slope (m)
0.75(Δy/Δx = 3/4)

Line rises from left to right (positive gradient)

Positive Slope

Angle (θ)

36.87°

inclination

Percent Grade

75%

civil / road grade

Distance (d)

5

between points

Midpoint (M)

(2, 1.5)

mid-coordinate
Standard Algebraic Line Equations
Slope-Intercept (y = mx + b):y = 0.75x + 0
Point-Slope Form:y - 0 = 0.75(x - 0)
Standard Form (Ax + By = C):-3x + 4y = 0
Perpendicular Slope

-1.3333

m_perp = −1/m
Line Angle

36.9° inclination

Standard Line Slope Formulas
Slope (m)
m =
y₂ − y₁x₂ − x₁
Slope-Intercepty = mx + b
Perpendicular Linem_perp = −1 / m
Step-by-Step Calculation Breakdown
Example: Point A (1, 2) and Point B (5, 10)
1. Calculate Rise: Δy = y₂ − y₁ = 10 − 2 = 8
2. Calculate Run: Δx = x₂ − x₁ = 5 − 1 = 4
3. Compute Slope m: 8 / 4 = 2.00
4. Percent Grade: (8 / 4) × 100 = 200%
Resulting Equation:y = 2x + 0 (y = 2x)

Key Geometric Concepts

  • Positive Slope: The line moves upward from left to right.
  • Negative Slope: The line descends from left to right.
  • Zero Slope: A perfectly horizontal line parallel to the x-axis.
  • Undefined Slope: A vertical line with zero horizontal change (division by zero).

Frequently Asked Questions

What is slope in coordinate geometry?
Slope (m) measures the rate of vertical change relative to horizontal change along a straight line: m = (y₂ − y₁) / (x₂ − x₁) = Rise / Run.
What does an undefined slope mean?
An undefined slope occurs when a line is perfectly vertical (x₁ = x₂). Because the horizontal change (Run) is 0, dividing by zero yields an undefined mathematical value (equation x = c).
What is the difference between slope and percent grade?
Slope is the direct ratio of Rise over Run (e.g. 0.05). Percent grade multiplies that ratio by 100% (e.g. 5% grade, common in civil road design and roofing).
How do you calculate the perpendicular slope?
The perpendicular slope is the negative reciprocal of the original slope: m_perp = −1 / m. If the original slope is 2/3, the perpendicular slope is −3/2 (−1.5).

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