Slope Calculator

Slope is evaluated from Point 1 - x₁, Point 1 - y₁ and Point 2 - x₂. The calculation reports Slope, Angle of Inclination and Grade / Gradient.

Results

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About the Slope Calculator

Slope is treated here as a quantitative relation between Point 1 - x₁, Point 1 - y₁, Point 2 - x₂ and Point 2 - y₂ and Slope, Angle of Inclination, Grade / Gradient and Y-Intercept.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
m = (y₂ - y₁) / (x₂ - x₁)
b = y - mx
Angle = arctan(m) in degrees

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

m = (y₂ - y₁) / (x₂ - x₁)
b = y - mx
Angle = arctan(m) in degrees

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: ADA Wheelchair Ramp Check

Inputs

x1: 0 y1: 0 x2: 60 y2: 4
Slope: 0.066667. Angle of Inclination: 3.8141 deg. Grade / Gradient: 6.67%. Y-Intercept: 0. Line Equation: y = 0x + 0

With Point 1 - x₁ = 0, Point 1 - y₁ = 0, Point 2 - x₂ = 60 and Point 2 - y₂ = 4 as the stated inputs, the result is Slope = 0.066667, Angle of Inclination = 3.8141 deg and Grade / Gradient = 6.67%. Each value corresponds to the declared output fields.

Example 2: Highway Grade — Mountain Pass

Inputs

x1: 0 y1: 5000 x2: 5280 y2: 5528
Slope: 0.1. Angle of Inclination: 5.7106 deg. Grade / Gradient: 10%. Y-Intercept: 5,000. Line Equation: y = 0x + 5000

With Point 1 - x₁ = 0, Point 1 - y₁ = 5,000, Point 2 - x₂ = 5,280 and Point 2 - y₂ = 5,528 as the stated inputs, the result is Slope = 0.1, Angle of Inclination = 5.7106 deg and Grade / Gradient = 10%. Each value corresponds to the declared output fields.

Example 3: Roof Pitch — 4/12 Pitch

Inputs

x1: 0 y1: 0 x2: 12 y2: 4
Slope: 0.333333. Angle of Inclination: 18.4349 deg. Grade / Gradient: 33.33%. Y-Intercept: 0. Line Equation: y = 0x + 0

With Point 1 - x₁ = 0, Point 1 - y₁ = 0, Point 2 - x₂ = 12 and Point 2 - y₂ = 4 as the stated inputs, the result is Slope = 0.333333, Angle of Inclination = 18.4349 deg and Grade / Gradient = 33.33%. Each value corresponds to the declared output fields.

Example 4: Line Equation — Algebra

Inputs

x1: 2 y1: 5 x2: 6 y2: 13
Slope: 2. Angle of Inclination: 63.4349 deg. Grade / Gradient: 200%. Y-Intercept: 1. Line Equation: y = 2x + 1

With Point 1 - x₁ = 2, Point 1 - y₁ = 5, Point 2 - x₂ = 6 and Point 2 - y₂ = 13 as the stated inputs, the result is Slope = 2, Angle of Inclination = 63.4349 deg and Grade / Gradient = 200%. Each value corresponds to the declared output fields.

Common Use Cases

  • Find slope of a ramp for ADA compliance
  • Calculate road grade percentage
  • Determine angle of inclination of a roof
  • Write equation of a line through two points