Calculate lever effort force, supported load, or arm length with N, kN, lbf, kgf, metric and imperial lengths, efficiency, and mechanical advantage.

Positive force magnitudes and perpendicular lever moment arms. Ideal efficiency is 100%; change the optional efficiency for a known loss estimate. This is not a lifting-equipment rating.

Optional settings

100% or blank assumes an ideal machine. Use a measured efficiency to estimate losses.

Effort Force Formula

The effort force is the input force you apply to move or lift a load. Choose a lever solve, known ideal mechanical advantage, pulley, or ramp. The formulas below are ideal; optional efficiency adjusts the required effort by dividing by efficiency as a fraction.

Mechanical Advantage Method

EF = L / MA
  • EF = effort force
  • L = load force
  • MA = mechanical advantage

Lever Method

EF = (L × LA) / EA
MA = EA / LA
  • EF = effort force
  • L = load force
  • LA = perpendicular distance from the pivot to the load force line of action
  • EA = perpendicular distance from the pivot to the effort force line of action
  • MA = mechanical advantage

Pulley Method

EF = L / S
MA = S
  • EF = effort force
  • L = load force
  • S = number of supporting rope segments
  • MA = mechanical advantage

Ramp Method

EF = L × (H / RL)
MA = RL / H
  • EF = effort force
  • L = load force
  • H = ramp height
  • RL = ramp length
  • MA = mechanical advantage

The lever modes compare perpendicular load and effort moment arms and can solve either force or arm. The known-advantage mode accepts ideal mechanical advantage directly. The pulley mode uses supporting rope segments; the ramp mode uses slope length divided by height. At the default 100% efficiency these are ideal models. A lower efficiency estimates aggregate losses; it does not predict friction, rope stretch, equipment strength, or a safe working load.

Common Mechanical Advantage Values

Setup Typical Ideal MA Effort Force Compared With Load
No mechanical advantage 1 Same as the load
2:1 lever, pulley, or ramp 2 One-half of the load
4:1 lever, pulley, or ramp 4 One-fourth of the load
5:1 ramp 5 One-fifth of the load

Force Unit Conversions

Unit Equivalent Common Use
N 1 newton SI force calculations
kN 1 kN = 1,000 N Large loads
lbf 1 lbf ≈ 4.44822 N US customary force calculations

Example Problems

Example 1: Effort force with mechanical advantage

You need to move a 600 N load with a mechanical advantage of 3.

EF = L / MA
EF = 600 / 3 = 200 N

The required effort force is 200 N.

Example 2: Effort force for a lever

A lever lifts a 500 N load. The load is 0.4 m from the pivot, and the applied effort is 1.6 m from the pivot.

EF = (L × LA) / EA
EF = (500 × 0.4) / 1.6 = 125 N

The required effort force is 125 N. The mechanical advantage is 1.6 / 0.4 = 4.

FAQ

What is effort force?

Effort force is the force you apply to a machine or tool to move a load. In a lever, it is the force applied to one side of the pivot. In a pulley, it is the pulling force on the rope. On a ramp, it is the force needed to push or pull the load up the incline.

Why is the real effort force sometimes higher than the calculated value?

At 100% efficiency the calculator uses ideal mechanical advantage. A measured efficiency can estimate aggregate losses, but real friction, bending, pulley bearing losses, rope drag, and surface resistance may vary. Actual effort may be higher; these estimates do not establish a safe working load.

Does a higher mechanical advantage always make lifting easier?

A higher mechanical advantage lowers the required effort force, but it usually increases the distance you must move. For example, a 4:1 pulley may require about one-fourth the force, but you may need to pull about four times as much rope in an ideal system.