In physics and engineering

**mechanical advantage (MA)**is the factor by which a machine multiplies the force put into it. The mechanical advantage can be calculated for the following simple machines by using the following formulas:

- Lever: MA = length of effort arm ÷ length of resistance arm.
- Wheel and Axle: A wheel is essentially a lever with one arm the distance between the axle and the outer point of the wheel, and the other the radius of the axle. Typically this is a fairly large difference, leading to an equally large mechanical advantage. This is why even simple wheels with wooden axles running in wooden blocks will still turn freely, because the friction is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.
- Pulley: Pulleys are wheels that are connected together with ropes. In doing so the direction of the force on the rope can be changed, with little loss in force due to friction (for the same reasons as the wheel). However pulleys can be "added together" to create additional mechanical advantage by having the rope looped over several pulleys in turn. A pulley with one rope (single fixed pulley) has an MA = 1, that is, no advantage (or disadvantage). A pulley with two ropes (single moveable pulley) has a MA = 2. A pulley with 6 ropes (block and tackle) has a MA = 6.
- Inclined Plane: MA = length of slope ÷ height of slope

- MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)

- (force in
**100**× distance in**6**) = (force out**600**× distance out**1**)

**WORK**

_{in}=

**WORK**

_{out}

This requires an ideal simple machine, meaning that there are no losses due to friction or elasticity. If friction or elasticity exist in the system *efficiency* will be lower; Work_{in} will be greater than Work_{out}

Mechanical advantage also applies to torque. A simple gearset is able to multiply torque.

There are two types of mechanical advantage: