Fulcrum Calculator

The fulcrum is the pivot point of a lever — the fixed point around which the beam rotates. It connects the lever to its support and determines how force is distributed between the effort side and the load side. Repositioning the fulcrum changes the mechanical advantage of the lever system.

Use the law of the lever: Fe × L1 = Fr × L2. If you know the effort force (Fe), load force (Fr), and total beam length (L), you can solve for L1 (effort arm) as L1 = Fr × L / (Fe + Fr). The fulcrum sits at that distance from the effort end. This calculator does that math for you automatically.

The law of the lever states that the product of force and arm length must be equal on both sides of the fulcrum: Fe × L1 = Fr × L2. This means a smaller force applied at a longer distance from the fulcrum can balance or lift a larger load placed closer to the fulcrum — the foundation of mechanical advantage.

For a mechanical advantage of 2 on a 1 m (1000 mm) lever, the effort arm (L1) must be twice the load arm (L2). Using L1 + L2 = 1000 mm and L1 = 2 × L2, you get L2 = 333 mm and L1 = 667 mm. The fulcrum should be placed 667 mm from the effort end (or 333 mm from the load).

Class 1 levers have the fulcrum between the effort and load (e.g., seesaw, crowbar) — MA can be greater or less than 1. Class 2 levers have the load between the fulcrum and effort (e.g., wheelbarrow) — MA is always greater than 1. Class 3 levers have the effort between the fulcrum and load (e.g., tweezers) — MA is always less than 1 but provides speed advantage.

The human elbow joint is a Class 3 lever. The fulcrum is at the elbow joint, the effort is applied by the bicep muscle just below the joint, and the load (object in hand) is at the end of the forearm. This gives a mechanical advantage less than 1, meaning you need more force than the load weighs, but you gain speed and range of motion.

The effort arm (L1) is the distance from the fulcrum to the point where effort force is applied. Using the lever equation: L1 = (Fr × L2) / Fe, where Fr is the load force, L2 is the load arm length, and Fe is the effort force. Alternatively, if you know the total beam length and load arm: L1 = L − L2.

Mechanical advantage (MA) is the ratio of output force (load) to input force (effort): MA = L1 ÷ L2. An MA greater than 1 means the lever amplifies your force — you lift more than you push. An MA less than 1 means you trade force for speed or distance. Understanding MA helps engineers design efficient lifting, actuating, and balancing systems.