Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. It is defined as the ratio between the equivalent output force $F_o$ achieved by the machine, and the input force $F_i$ supplied to the machine:

$\mathrm{MA} \= \frac{F_o}{F_i}$.

A simple machine is one of the six basic non-motorized devices identified by Renaissance scientists drawing from Greek texts on technology:

These simple machines provide a mechanical advantage by changing the direction or magnitude of a force. Simple machines can be combined with other devices to form more complicated machines and can thus be considered the building blocks of engineering.

An inclined plane is a simple machine that provides mechanical advantage by reducing the force required to lift an object. However, the reduced force must be applied over a longer distance. The machine consists of a flat surface that is tilted by an angle such that one end of the surface is higher than the other.

For a frictionless inclined plane the amount of effective work done equals the potential energy gained, which is proportional to the vertical displacement $h$, that is,

$W\=m g h$.

On the other hand, the actual work done can be calculated as the product of the force applied and the distance, $l$, traveled along the inclined plane:

$W \= F_i l$.

Since the effective force overcome is the object's weight, $F_o \= m g$, the mechanical advantage works out to

$\mathrm{MA}\mathit{ }\= \frac{F_o}{F_i}\=\frac{l}{h}$.

Given that

$\sin \left(\mathrm{\θ}\right) \= \frac{h}{l}$,

where, $\mathrm{\θ}$ is the angle of inclination, the mechanical advantage can also be represented by:

$\frac{1}{\sin \left(\mathrm{\θ}\right)}$,

With the addition of friction opposing the movement of the mass, the mechanical advantage is reduced as some of the input energy is converted to heat. As a result, more effort is required in order to push the object up the inclined plane.

A wedge is a simple machine that is made up of two inclined planes forming a triangular shape. It provides mechanical advantage by converting the force applied at its end into forces perpendicular to the inclined surfaces. As such, a wedge is a good tool to cut objects (for example, an axe), hold objects in place (for example, a doorstopper), and lift objects in order to separate them from the surface they are resting on.

Similar to an inclined plane, the mechanical advantage for a wedge is the ratio of the length of its slope to its height:

$\mathrm{MA} \= \frac{l}{h}$.