Lever Calculator
Enter a load, a load arm, and an effort arm to get the force you need to push and the mechanical advantage — and see why a longer arm makes the work easier.
Force and advantage at once
Enter the load, the load arm, and the effort arm and the calculator returns the required effort in newtons and the mechanical advantage together.
Use SI units
Force in newtons and distances in metres keep the moments consistent — a 10 kg mass weighs about 98 N (kilograms × 9.81).
What is the law of the lever?
Balancing moments around a pivot
This lever calculator uses the law of the lever: a rigid bar balances around a pivot when the load times its distance from the pivot equals the effort times its distance. Because force multiplied by distance is the turning effect (the moment), a long effort arm lets a small push balance a large load on a short arm. Give the calculator the load in newtons, the load arm, and the effort arm in metres, and it returns the effort force you must apply plus the mechanical advantage.
Enter a load and the two arm lengths to get the required effort in newtons and the mechanical advantage instantly.
The lever balances when the two moments are equal, so the effort is the load moment divided by the effort arm, and the mechanical advantage is the ratio of the two arms.
effort = (load × loadArm) ÷ effortArmSuppose you balance a 100 N load sitting 0.5 m from the pivot, pushing on an effort arm 2 m long. The load moment is 100 × 0.5 = 50 N·m. Divide by the 2 m effort arm and you need only (100 × 0.5) ÷ 2 = 25 N — a quarter of the load. The mechanical advantage is the arm ratio, 2 ÷ 0.5 = 4, so the lever multiplies your force fourfold. A longer effort arm or a shorter load arm raises that advantage and lowers the effort you need.
The formula is exact for an ideal lever, but a couple of practical points are worth keeping in mind.
Ideal lever and consistent units
This calculator models an ideal, rigid, weightless lever with a frictionless pivot and forces acting straight down on the arms. Real levers lose a little to friction and the bar's own weight, and angled forces use the perpendicular distance to the pivot. Keep your units consistent — newtons for force and metres for both arms — or the moments will not balance.