Top

Centroid Calculator
Top
Centroid Calculator is an online tool used to determine the centroid of any triangle when the vertices are known.
Centroid of the Triangle
The centroid of the triangle is the intersection of the medians of a triangle. If we have an object then the centroid of that object is its centre. The triangle’s centroid separates the median in the ratio 2:1. The average of the x-coordinate’s value and the average of the y-coordinate’s value is the centroid of the triangle.
 

Step by Step Calculation

Back to Top
Step 1 :  

If A(x1, y1) , B(x2, y2) and C(x3, y3) are the vertices of a triangle then the centroid of the triangle is

($\frac{(x_{1}+ x_{2} + x_{3})}{3}$, $\frac{(y_{1} + y_{2} + y_{3})}{3}$).



Step 2 :  

To find the centroid of the triangle, use above formula and calulate it further.



Example Problems

Back to Top
  1. Find the centroid of the triangle whose vertices are A (4, 10), B (6, 1) and C (9, 0).


    Step 1 :  

    Given: Centroid of the triangle whose vertices are A (4, 10), B (6, 1) and C (9, 0).


     


    Centroid triangle formula = ($\frac{(x_{1}+ x_{2} + x_{3})}{3}$, $\frac{(y_{1} + y_{2} + y_{3})}{3}$).


     


    A (4, 10) as A (x1, y1)

    B (6, 1) as B (x2, y2)

    C (9, 0) as C (x3, y3)



    Step 2 :  

    Put the values in the formula and solve it further.


     


    Centroid triangle formula = ($\frac{(4+6+9)}{3}$, $\frac{(10+1+0)}{3}$)


    = ($\frac{19}{3}$, $\frac{11}{3}$)


    = (6.33, 3.67)


    The centroid of the triangle with vertices A (4, 10), B (6, 1) and C (9, 0) is (6.33, 3.67).



    Answer  :  

    Centroid of the triangle: (6.33, 3.67)



  2. Find the centroid of the triangle whose vertices are A (-6, -9), B (1, 6) and C (14, 5).


    Step 1 :  

    Given:Centroid of the triangle whose vertices are A (-6, -9), B (1, 6) and C (14, 5).


     


    Centroid triangle formula = ($\frac{(x_{1}+ x_{2} + x_{3})}{3}$, $\frac{(y_{1} + y_{2} + y_{3})}{3}$).


     


    A (-6, -9) as A (x1, y1)




    B (1, 6) as B (x2, y2)




    C (14, 5) as C (x3, y3)



    Step 2 :  

    Put the values in the formula and solve it further.


     


    Centroid triangle formula = ($\frac{(-6+1+14)}{3}$, $\frac{(-9+6+5)}{3}$)




    = ($\frac{9}{3}$, $\frac{2}{3}$)




    = (3, 0.67)




    The centroid of the triangle with vertices A (-6, -9), B (1, 6) and C (14, 5) is (3, 0.67).



    Answer  :  

    Centroid of the triangle: (3, 0.67)



*AP and SAT are registered trademarks of the College Board.