tooljar

    Center of Mass Calculator

    Calculate the center of mass for point masses and uniform shapes

    Quick examples:
    Quick examples:
    #1
    #2

    Visualization

    2.4 m
    X coordinate
    0 m
    Y coordinate
    5 kg
    Total Mass
    Position: (2.4, 0) m

    Formula

    x_cm = Σ(m_i × x_i) / Σm_i
    y_cm = Σ(m_i × y_i) / Σm_i

    About Center of Mass

    The center of mass is the weighted average position of all mass in a system. It's the point where the entire mass of an object can be considered to be concentrated.

    • For point masses, the center of mass is calculated using the weighted average of each mass's position.
    • For uniform shapes with constant density, the center of mass coincides with the geometric center (centroid).
    • The center of mass is the balance point - if you support an object at this point, it will be perfectly balanced.
    • Understanding center of mass is crucial in physics, engineering, robotics, and sports biomechanics.