A machine has mechanical advantage when it trades one kind of motion for another so that a smaller input force can balance or produce a larger output force.

The force mechanical advantage is

$$MA=\frac{F_{\mathrm{out}}}{F_{\mathrm{in}}}.$$

Levers

For an ideal lever in static equilibrium, moments about the fulcrum balance:

$$F_{\mathrm{in}}r_{\mathrm{in}}=F_{\mathrm{out}}r_{\mathrm{out}}.$$

A longer input lever arm therefore reduces the input force needed for a given output force.

Pulleys

In an ideal rope, the tension is the same throughout. A moving load supported by several rope segments receives an upward force from each segment, so the ideal mechanical advantage equals the number of supporting segments.

Gears

Meshing gears exchange torque and angular displacement. For ideal gears, a larger driven gear can produce greater output torque at lower angular speed.

The trade-off

Mechanical advantage does not create energy. In an ideal lossless machine, reducing the required input force requires the input point to move farther or faster than the output.