Triangle vertices

Calculator and formulas for calculating angles of triangle vertices with 3 points

Triangle vertices calculation


This function calculates the angles, the area and the side lengths of a triangle that is defined in the coordinate system. Enter the values of the x / y coordinates of the three vertices. Then click on the 'Calculate' button.


Triangle vertices calculator

 Input
Vertex A (x1, y1)
Vertex B (x2, y2)
Vertex C (x3, y3)
Decimal places
 Results
Area A
Perimeter U
Side length a
Side length b
Side length c
Angle α
Angle β
Angle γ

Formulas for triangle vertices calculation

Area \(\displaystyle A\)

\(\displaystyle A= \frac{1}{2}|[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|\)
Side length \(\displaystyle a\)
\(\displaystyle a=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
Side length \(\displaystyle b\)
\(\displaystyle b=\sqrt{(x_2-x_3)^2+(y_2-y_3)^2}\)
Side length \(\displaystyle c\)
\(\displaystyle c=\sqrt{(x_3-x_1)^2+(y_3-y_1)^2}\)
Perimeter \(\displaystyle P\)
\(\displaystyle P=a+b+c\)
Angle \(\displaystyle α\)
\(\displaystyle α=arccos\left(\frac{b^2+c^2-a^2}{2bc}\right)\)
Angle \(\displaystyle β\)
\(\displaystyle β=arccos\left(\frac{a^2+c^2-b^2}{2ac}\right)\)
Angle \(\displaystyle γ\)
\(\displaystyle γ=arccos\left(\frac{a^2+b^2-c^2}{2ab}\right)\)
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