Slope Calculator Online
Calculate line slope m, inclination angle, grade percentage, and equation y = mx + b.
Input Parameters
Live Result
Details
Steps
Coordinates: Point 1 = (2, 3), Point 2 = (6, 11)
Slope Formula: m = (y₂ - y₁) / (x₂ - x₁)
Calculate Rise (Δy): 11 - (3) = 8
Calculate Run (Δx): 6 - (2) = 4
Compute Slope: m = 8 / 4 = 2
Y-Intercept (b = y₁ - m·x₁): 3 - (2 × 2) = -1
Slope-Intercept Equation: y = 2x - 1
Angle of Inclination: θ = arctan(2) = 63.4349°
Distance: d = √(Δx² + Δy²) = √(80) = 8.9443
Quick Answer & Understanding Your Result
A Slope Calculator determines the steepness, incline, and direction of a straight line connecting two points: m = (y₂ - y₁) / (x₂ - x₁) = Rise / Run. If the change in x is zero (Δx = 0), the line is vertical and the slope is mathematically Undefined.
Slope Types & Geometric Meanings
- Positive Slope (m > 0): The line rises upwards from left to right.
- Negative Slope (m < 0): The line falls downwards from left to right.
- Zero Slope (m = 0): A perfectly horizontal line parallel to the x-axis (y = c).
- Undefined Slope (Vertical): A vertical line parallel to the y-axis with angle θ = 90° (x = c).
Companion Line Representations
- Slope-Intercept Form: y = mx + b, where b is the y-intercept.
- Angle of Inclination: θ = arctan(m) measured in degrees or radians.
- Grade Percentage: Grade % = m × 100% used in civil engineering and road grading.
Enter the coordinates of two points above to compute slope, angle, line equations, and distance instantly.
Formula & Calculation Logic
Mathematical FormulaThe slope is the ratio of vertical change (rise) to horizontal change (run). The y-intercept b is calculated as y₁ - m × x₁.
Step-by-Step Guide
Enter Coordinates
Input coordinates for Point 1 (x₁, y₁) and Point 2 (x₂, y₂).
Calculate Rise and Run
Find vertical difference Δy = y₂ - y₁ and horizontal difference Δx = x₂ - x₁.
Compute Slope
Divide rise by run: m = Δy / Δx (checking for vertical zero division).
Review Equations
View slope-intercept form y = mx + b, angle θ, and road grade percentage.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Points (2, 3) and (6, 11) | Rise = 11 - 3 = 8, Run = 6 - 2 = 4. Slope m = 8 / 4 = 2. | ||
| Horizontal Line: (1, 5) and (8, 5) | Rise = 5 - 5 = 0. Slope m = 0 / 7 = 0. | ||
| Vertical Line: (4, -1) and (4, 9) | Run = 4 - 4 = 0. Division by zero is undefined. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Wolfram MathWorld - Slope
NIST Digital Library of Mathematical Functions
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: m = (y₂ - y₁) / (x₂ - x₁)
Last Reviewed: August 21, 2026
Primary Source: Wolfram MathWorld - Slope
Reference Document: NIST Digital Library of Mathematical Functions
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.