How does an inclined plane reduce the force needed to raise an object?

An inclined plane is a simple machine consisting of a sloping surface that allows an object to be raised with less force than would be required to lift it vertically.

The force ($F$) needed to move an object of weight ($W$) up an incline (discounting friction) is determined by the angle of the slope ($\theta$) relative to the horizontal, expressed by the formula:

$$F=W\sin \theta$$

Because the sine of an angle between 0 and 90 degrees is always less than 1, the required force is less than the actual weight of the object.1

This reduction in force is a trade-off inherent to machines. While the inclined plane provides a mechanical advantage by amplifying force, the input force must be applied over a longer distance compared to a direct vertical lift. Essentially, what is gained in force is lost in the distance over which that force must be applied. The shallower the slope, the less force is required, but the longer the distance the object must travel to reach the same height.21