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How is the efficiency of a machine calculated from input and output work?

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A diagram displays six types of simple machines with labeled illustrations: inclined plane, wedge, screw, lever, wheel and axle, and pulley, each shown with real-world examples like ramps, axes, screws, seesaws, door handles, and pulleys lifting objects. — simple machine Six simple machines for transforming energy into work.

The efficiency of a machine is defined as the ratio of the work output to the work input. Because of friction, the work output is always less than the work input, meaning the efficiency of a machine is always less than 100 percent.1

Mathematically, work is calculated as the product of the applied force and the distance moved in the direction of that force ( $W = F \times S$ ). While efficiency can be determined by comparing the work output to the work input, this requires knowing the average forces over a specific distance, which can be inconvenient to measure.21

In practice, efficiency is more easily determined using power formulas, which measure the rate at which work is performed. For mechanical systems, efficiency is typically expressed as the ratio of the power delivered by the system to the power supplied to it.13