Perimeter of a Triangle Given Vertices Calculator
Enter the x and y coordinates of three vertices A, B and C to instantly find each side length, the total perimeter, and the area of the triangle.
Sum of all three side lengths
- 1
Side AB (distance formula)
√[(4)² + (0)²] = 4Euclidean distance between vertex A and vertex B. - 2
Side BC
√[(-2)² + (3)²] = 3.6056 - 3
Side CA
√[(-2)² + (-3)²] = 3.6056 - 4
Perimeter = AB + BC + CA
4 + 3.6056 + 3.6056 = 11.2111
How does this calculator work?
Give each vertex's (x, y) coordinates; the calculator uses the distance formula d = √[(Δx)²+(Δy)²] on each pair of vertices and sums the three side lengths to get the perimeter. The area is also returned via the shoelace formula.
Formula
How this is calculated
Each side of the triangle is the straight-line (Euclidean) distance between two vertices, computed with the distance formula: d = √[(Δx)² + (Δy)²]. Squaring the horizontal and vertical differences, summing them, and taking the square root converts the two-coordinate gap into a single length — a direct generalisation of the Pythagorean theorem to any orientation in the plane.
The perimeter is the sum of all three side lengths. This calculator also computes the area using the shoelace formula, ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|, which gives the signed area from any list of vertices in order, scaled to positive. No separate height or angle measurement is needed.
If the three points are collinear — all lying on a single line — the area is zero and no valid triangle exists, so the result is hidden. Coordinates can be any real numbers, including negatives and decimals. Units are whatever units you use for the coordinates; if you enter metres, the perimeter and side lengths are in metres and the area is in square metres.
Frequently asked questions
The distance between two points (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)²+(y₂−y₁)²]. It follows directly from the Pythagorean theorem applied to the horizontal and vertical separations between the points.
The three points may be collinear — all sitting on the same line — which gives a degenerate triangle with zero area. Adjust at least one vertex so the three points form a proper triangle.
Yes. The distance formula works for any real-number coordinates. Negative coordinates simply place the vertex in a different quadrant of the Cartesian plane.
Also known as
TG we-Calculate Editorial Team. (2026). Perimeter of a Triangle Given Vertices Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/perimeter-of-a-triangle-with-vertices-calculator
TG we-Calculate Editorial Team. "Perimeter of a Triangle Given Vertices Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/perimeter-of-a-triangle-with-vertices-calculator.
TG we-Calculate Editorial Team, "Perimeter of a Triangle Given Vertices Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/perimeter-of-a-triangle-with-vertices-calculator
@misc{wecalculate_perimeter_of_a_triangle_with_vertices_calculator, title = {Perimeter of a Triangle Given Vertices Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/perimeter-of-a-triangle-with-vertices-calculator}}, year = {2026}, note = {TG we-Calculate} }
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