Fulcrum Calculator

Set the torques equal: $$F_1 d_1 = F_2 d_2$$. With $$d_1 + d_2 = L$$, solve for $$d_1 = F_2 L / (F_1 + F_2)$$. The fulcrum is always closer to the larger force, since it needs a shorter moment arm to produce the same torque.

Torque equals force times distance. A larger force produces the same torque with a shorter arm. To balance the system, the larger force must be at a shorter distance from the pivot, so the fulcrum naturally shifts toward the heavier side.

Yes. A uniform beam of mass $$m_b$$ acts as though its weight $$m_b g$$ is concentrated at its center. This adds a third torque term to the balance equation and shifts the fulcrum position accordingly. This calculator assumes an ideal massless beam.

In this model with two downward forces at the beam ends, the fulcrum must be between them (0 < x < L). If one force were upward, the fulcrum could lie outside the beam, but that represents a different mechanical configuration.

For two point masses at the beam ends, the fulcrum position that balances them is exactly the center of mass of the two-mass system. This is because the center of mass is at $$x_{cm} = \frac{m_2 L}{m_1 + m_2}$$ from mass 1, which matches the fulcrum formula when forces are weights.