Triangle Slope Calculator
Calculate slopes using triangle method or find the slope of a triangle itself
Slope Calculation
Triangle Slope Results
Slope Calculation Examples
Triangle Slope - Using Sides
Given: Rise (a) = 3, Run (b) = 4
Formula: slope = rise/run = a/b
Calculation: slope = 3/4 = 0.75
Result: Slope = 0.75, Angle = 36.87°, Grade = 75%
Triangle Slope - Using Angle
Given: Angle α = 30°
Formula: slope = tan(α)
Calculation: slope = tan(30°) = 0.577
Result: Slope = 0.577, Grade = 57.7%
Line Slope - Using Points
Given: Point 1 (1, 2), Point 2 (5, 8)
Formula: slope = (y₂ - y₁)/(x₂ - x₁)
Calculation: slope = (8 - 2)/(5 - 1) = 6/4 = 1.5
Result: Slope = 1.5, Rise = 6, Run = 4
Slope Calculation Methods
Rise over Run
slope = rise/run = a/b
Tangent of Angle
slope = tan(α)
Cotangent of Angle
slope = cot(β) = 1/tan(β)
Slope Properties
Positive Slope
Line rises from left to right
Negative Slope
Line falls from left to right
Zero Slope
Horizontal line
Undefined Slope
Vertical line
Quick Tips
Rise is the vertical change (up/down)
Run is the horizontal change (left/right)
Slope = tan(angle) for right triangles
Steeper slopes have larger absolute values
Understanding Triangle Slope
What is a Slope Triangle?
A slope triangle is a right triangle formed by drawing horizontal and vertical lines from two points on a line. This creates a visual representation that helps calculate the slope using the rise over run formula.
Triangle Slope Methods
- •Sides Method: Use rise/run = a/b where a is vertical side, b is horizontal side
- •Angle α Method: Use slope = tan(α) where α is angle at horizontal side
- •Angle β Method: Use slope = cot(β) where β is angle at vertical side
Mathematical Formulas
Basic Slope Formula
slope = rise/run = (y₂ - y₁)/(x₂ - x₁)
Triangle Slope Formula
slope = a/b = tan(α) = cot(β)
Angle Conversion
angle = arctan(slope) × 180/π
Applications
- • Surveying and construction
- • Road grade calculations
- • Roof pitch determination
- • Physics and engineering