Fulcrum Calculator
Find fulcrum position for lever balance from forces, distances, and moments with step-by-step torque equations.
What Is a Fulcrum?
A fulcrum is the pivot point of a lever. For a beam in static equilibrium, the torques (moments) about the fulcrum must balance: F1 × d1 = F2 × d2, where F1 and F2 are forces and d1 and d2 are their distances from the fulcrum. This principle underlies seesaws, balance scales, and mechanical advantage systems.
Lever Balance Equation
When two loads act on a beam of total length L, the fulcrum position from the F1 side is d1 = F2 × L / (F1 + F2). Heavier loads sit closer to the fulcrum; lighter loads sit farther away. The calculator can also solve for unknown forces or total length.
Applications
- Balance scales: Equal-arm or unequal-arm scales use torque balance to measure mass.
- Construction: Finding support points for beams and scaffolding under uneven loads.
- Physics education: Demonstrating torque, equilibrium, and mechanical advantage.
Related tools: Force Calculator and Friction Calculator.
Frequently Asked Questions
What units should I use for force and distance?
Use consistent units: newtons (N) for force and meters (m) for distance. Torque is then in newton-meters (N·m). Any consistent force-length pair works as long as both sides match.
Does the beam weight matter?
This calculator assumes a weightless beam with point loads. If the beam has significant mass, include its weight as an additional load at its center of gravity.
What if there are more than two forces?
For multiple loads, sum all clockwise moments and set them equal to all counterclockwise moments. This tool handles the two-force case, which is the most common introductory problem.
How is this related to mechanical advantage?
A lever multiplies force at the cost of distance. The ratio d1/d2 gives the mechanical advantage when F1 is the effort and F2 is the load.
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