Triangle Slope Calculator — Slopes of All Three Sides from Vertices
Enter the coordinates of vertices A, B, C to get the slope (gradient), length, and interior angle of each side, alongside the area and perimeter of the triangle.
Rise / run along side AB
- 1
Rise (Δy = y_B − y_A)
0 − 0 = 0 - 2
Run (Δx = x_B − x_A)
4 − 0 = 4 - 3
Slope of AB = rise ÷ run
0 ÷ 4 = 0A positive slope rises left to right; a negative slope falls.
How does this calculator work?
For a triangle with vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃): slope of AB = (y₂−y₁)/(x₂−x₁) and similarly for BC, CA. Side lengths use the distance formula. Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|. Enter all three vertices to get every slope, length, angle, area and perimeter at once.
Formula
How this is calculated
The slope (gradient) of a line segment between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ − y₁) / (x₂ − x₁). It measures how much the segment rises (or falls) for every unit it moves horizontally. A vertical segment has an undefined slope because the denominator is zero; any other slope is a finite real number, including zero for a horizontal segment.
A triangle in the coordinate plane has three sides — AB, BC, CA — each with its own slope. These slopes are generally all different unless two sides happen to be parallel (which would make the "triangle" degenerate). The calculator evaluates each slope directly from the vertex coordinates, then also computes each side's length via the distance formula and each interior angle via the Law of Cosines.
The area is computed from the Shoelace (surveyor's) formula: Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. If this equals zero the three points are collinear and no real triangle exists, so the calculator returns a warning.
Frequently asked questions
A side is vertical if both its endpoints have the same x-coordinate. The slope formula divides by x₂ − x₁ = 0, which is undefined. Vertical sides are perfectly valid — the calculator labels them "undefined (vertical)" rather than returning an error.
No — if two sides were parallel they would never meet at a vertex, so no triangle could be formed. All three slopes of a valid (non-degenerate) triangle are distinct, though two of the three sides could approach parallelism in a very flat triangle.
The Shoelace formula gives Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. It is exact for any triangle regardless of orientation and does not require computing side lengths first.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Slope Calculator — Slopes of All Three Sides from Vertices [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-slope-calculator
TG we-Calculate Editorial Team. "Triangle Slope Calculator — Slopes of All Three Sides from Vertices." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-slope-calculator.
TG we-Calculate Editorial Team, "Triangle Slope Calculator — Slopes of All Three Sides from Vertices," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-slope-calculator
@misc{wecalculate_triangle_slope_calculator, title = {Triangle Slope Calculator — Slopes of All Three Sides from Vertices}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-slope-calculator}}, year = {2026}, note = {TG we-Calculate} }
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