Lever Calculator

Enter the load force and the load/effort arm lengths measured from the fulcrum to find the effort force required, the mechanical advantage, and the fulcrum torque using the law of the lever.

Quick Facts

Law of the Lever
F_effort × d_effort = F_load × d_load
Torques (moments) about the fulcrum must balance for the lever to sit in equilibrium.
Mechanical Advantage
MA = d_effort / d_load
MA > 1 means the lever multiplies force; MA < 1 means it multiplies speed/distance instead.
Three Lever Classes
1st, 2nd, and 3rd class
Classified by whether the fulcrum, load, or effort sits in the middle (seesaw, wheelbarrow, forearm).

Your Results

Calculated
Effort Force Required
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F_effort = (F_load × d_load) / d_effort
Mechanical Advantage
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MA = d_effort / d_load = F_load / F_effort
Moment at the Fulcrum
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Torque balance: F_load × d_load = F_effort × d_effort
Lever Action
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Whether this lever trades effort for distance, or the reverse

Ready

Enter the load force and both arm lengths (measured from the fulcrum), then press Calculate.

Formula and Method for the Lever Calculator

A lever is a rigid bar that pivots on a fixed point called the fulcrum. Pushing down on one end (the effort) lets you lift or balance a load applied on the other end. This calculator uses the law of the lever — a statement of rotational (torque) equilibrium — to find the effort force needed to balance a given load: Feffort × deffort = Fload × dload, where dload and deffort are the perpendicular distances from the fulcrum to the load and to the effort, respectively.

How the calculation works

Enter the load force and the distances from the fulcrum to the load and to the effort (the load arm and effort arm). Solving the torque-balance equation for the unknown gives the required effort force: Feffort = (Fload × dload) / deffort. The calculator also reports the mechanical advantage, MA = deffort / dload = Fload / Feffort, the moment (torque) at the fulcrum, Fload × dload (which equals Feffort × deffort when the lever is balanced), and whether the lever is acting as a force multiplier (MA > 1) or a speed/distance multiplier (MA < 1). The model assumes an ideal, rigid, massless, frictionless lever — the standard simplification used in introductory mechanics.

Common mistakes

  • Measuring from the wrong point: both arm lengths must be measured from the fulcrum (pivot), not from the ends of the lever or from each other.
  • Mixing length units: the load arm and effort arm must use the same unit — convert inches to feet, or centimeters to meters, before entering either value.
  • Treating mechanical advantage as fixed: MA depends entirely on where the fulcrum sits relative to the load and effort — moving the fulcrum changes MA even on the same physical bar.
  • Ignoring real-world losses: friction at the pivot and the lever's own weight reduce the actual mechanical advantage below the ideal value this calculator reports.

Real-world applications

  • First-class levers (fulcrum between load and effort): seesaws, crowbars, scissors, and claw hammers pulling nails.
  • Second-class levers (load between fulcrum and effort): wheelbarrows, bottle openers, and nutcrackers — these always have MA > 1.
  • Third-class levers (effort between fulcrum and load): a human forearm lifting a weight, fishing rods, tweezers, and shovels — these always have MA < 1, trading force for reach and speed.
  • Engineering design: the moment (torque) result tells designers how much bending load the fulcrum, pin, or hinge must withstand without failing.

Frequently Asked Questions

What is the law of the lever?
The law of the lever states that a lever is in rotational equilibrium when the moments (torques) on each side of the fulcrum are equal: F_effort × d_effort = F_load × d_load, where each distance is measured from the fulcrum to the point where that force is applied.
What is mechanical advantage in a lever?
Mechanical advantage (MA) is the ratio of the effort arm to the load arm: MA = d_effort / d_load = F_load / F_effort. An MA greater than 1 means the lever lets you lift a load with less effort force than the load's weight; an MA less than 1 means the effort force must exceed the load, but the effort end moves farther and faster.
What are the three classes of levers?
First-class levers have the fulcrum between the load and the effort (a seesaw or crowbar). Second-class levers have the load between the fulcrum and the effort (a wheelbarrow or bottle opener). Third-class levers have the effort between the fulcrum and the load (a human forearm, a fishing rod, or a pair of tweezers).
Does a lever reduce the amount of work needed?
No. An ideal, frictionless lever does not change the total work (energy) required — it only trades force for distance. Whatever effort force you save by using a longer effort arm, you pay back by moving that end of the lever a proportionally greater distance.

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