Fulcrum Calculator

A fulcrum is the pivot around which a lever rotates. When downward forces act on opposite sides, the lever balances only when their moments, or torques, about the fulcrum are equal. This calculator locates that balance point between two forces separated by a known distance. It assumes a rigid, weightless lever, perpendicular forces, and a frictionless pivot. If the left force is F1, the right force is F2, and their total separation is L, equilibrium requires F1d1 = F2d2 and d1 + d2 = L. Solving these equations gives d1 = F2L/(F1 + F2) and d2 = F1L/(F1 + F2). The larger force must be closer to the fulcrum, while the smaller force acts through a longer arm. Equal forces place the fulcrum exactly halfway between them. Force may be entered in newtons and separation in meters as labeled, although the geometric ratio is unchanged if both forces share another unit and all lengths share another unit. The displayed distances follow the entered length unit conceptually, but the interface identifies meters to avoid accidental mixing. If values originate as masses, multiply each mass by the same gravitational acceleration. Since that common factor cancels, masses measured in the same unit can also be compared as proportional loads when local gravity is identical. Real levers add complications. The beam has weight acting at its center of gravity, applied forces may be angled, bearings create friction, and supports have finite width. Each additional load contributes its own signed moment and cannot be represented by this two-load equation without first combining forces and moments correctly. Use this calculator for seesaws, simple balance beams, conceptual statics problems, and preliminary layouts. For structural lifting devices, include self-weight, dynamic loading, material strength, support reactions, and an appropriate safety factor before selecting hardware or approving safe operation.