Centre of Mass Calculator

This page provides insight into determining the centre of mass and some functions to help you calculate it.
CalculationInputs﻿﻿Mass, a
:2g​
﻿
﻿﻿Mass, b
:4g​
﻿
﻿﻿Distance, d
:6m​
﻿
Here are the variables for the equation
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Output﻿﻿X coordinate for centre, R(x)
:4​
﻿
﻿
Rx=(maxa+mbxb)ma+mb=mbdma+mbR_x = \frac{(m_ax_a + m_bx_b)}{m_a+m_b} = \frac{m_bd}{m_a + m_b}Rx​=ma​+mb​(ma​xa​+mb​xb​)​=ma​+mb​mb​d​
ExplanationThe centre of mass is a position defined relative to an object or system of objects. It is the average position of all parts or objects of a system, weighted according to their masses.
This is demonstrated by the diagram below, depicting the coordinate system of an object:
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Figure 1: Diagram of a Coordinate System
The centre of mass is located at the centroid for simple rigid objects with uniform density and can be calculated with the following formula:
﻿
Rx=(maxa+mbxb)ma+mb=mbdma+mbR_x = \frac{(m_ax_a + m_bx_b)}{m_a+m_b} = \frac{m_bd}{m_a + m_b}Rx​=ma​+mb​(ma​xa​+mb​xb​)​=ma​+mb​mb​d​
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