Centre of Gravity Calculator

This calculation tool is designed to help you quickly and accurately determine the centre of gravity. 
CalculationCentre of Gravity From a Given PerimeterThis function calculates the centre of gravity of a body given a perimeter, like a triangle.
The centre of gravity is the centre of a circle inside a given triangle ABC, the middle points of the sides of the triangle.
Inputs﻿﻿Height, h
:3.00m​
﻿
﻿﻿Distance, a
:10.00m​
﻿
﻿
d=h(b+c)2(a+b+c)d= \frac{h(b+c)}{2(a+b+c)}d=2(a+b+c)h(b+c)​
Here are the variables for the equation
d = distance to the geometric centre.
h = perpendicular height of the triangle.
a = side length of the triangle.
b = side length of the triangle.
c = side length of the triangle.
﻿﻿Distance, b
:15.00m​
﻿
﻿﻿Distance, c
:20.00m​
﻿
﻿
Figure 1: Diagram of the Triangle in Calculating the Centre of Gravity
Output﻿﻿Centre, d
:1.17meter​
﻿
﻿
Triangle Centre of Gravity CalculationA simpler calculator is as follows to calculate the centre of gravity of a triangle.
The centre of gravity of a triangle is the intersection of lines BE and AD (as seen in the diagram).
Inputs﻿﻿Height, h (triangle)
:30.00m​
﻿
﻿
a=h3a= \frac{h}{3}a=3h​
Here are the variables for the equation
a = distance to the geometric centre.
h = perpendicular height of the triangle.
﻿
Figure 2: Diagram of the Triangle in Calculating the Centre of Gravity
Outputs﻿﻿Centre, a (triangle)
:10.00meter​
﻿
﻿
Two Bodies Centre of Gravity CalculationThis function calculates the centre of gravity of two separate bodies, as a function of the masses and the distance between the centre of the bodies.
Inputs﻿﻿Mass, Q
:100.00g​
﻿
﻿﻿Mass, P
:150.00g​
﻿
﻿﻿Distance, a (two bodies)
:50.00m​
﻿
﻿
b=Q×aP+Qb= \frac{Q\times a}{P+Q}b=P+QQ×a​
﻿
c=P×aP+Qc= \frac{P\times a}{P+Q}c=P+QP×a​
Here are the variables for the equation
Q, P = the mass. i.e. Q is the body in Figure 1.
a = the distance between the centre point of the two bodies. 
﻿
Figure 3: Diagram of Two Bodies in Calculating the Centre of Gravity
Outputs﻿﻿Centre, b (two bodies)
:20.00​
﻿
﻿﻿Centre, c (two bodies)
:30.00​
﻿
ExplanationThe centre of gravity refers to the point in a body, like a volume, area or line, that would be in balance if it were suspended. In a symmetrical body of a uniform material, the centre of gravity is the geometric centre.
For a parallelogram, the centre of gravity is at the intersection of the diagonals.
For more complex shapes, there are different equations to calculate the centre of gravity of different bodies, like from the perimeter of a triangle and for two bodies.
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