Efficiency is the (often measurable) ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without waste. In more mathematical or scientific terms, it is a measure of the extent to which input is well used for an intended task or function (output). It often specifically comprises the capability of a specific application of effort to produce a specific outcome with a minimum amount or quantity of waste, expense, or unnecessary effort. Efficiency, of course, refers to very different inputs and outputs in different fields and industries.
Efficiency is very often confused with effectiveness. In general, efficiency is a measurable concept, quantitatively determined by the ratio of useful output to total input. Effectiveness is the simpler concept of being able to achieve a desired result, which can be expressed quantitatively but doesn't usually require more complicated mathematics than addition. Efficiency can often be expressed as a percentage of the result that could ideally be expected, for example if no energy were lost due to friction or other causes, in which case 100% of fuel or other input would be used to produce the desired result. This does not always apply, not even in all cases in which efficiency can be assigned a numerical value, e.g. not for specific impulse.
A common but confusing way of distinguishing between efficiency and effectiveness is the saying "Efficiency is doing things right, while effectiveness is doing the right things." This saying indirectly emphasizes that the selection of objectives of a production process is just as important as the quality of that process. This saying popular in business however obscures the more common sense of "effectiveness", which would/should produce the following mnemonic: "Efficiency is doing things right; effectiveness is getting things done." This makes it clear that effectiveness, for example large production numbers, can also be achieved through inefficient processes if, for example, workers are willing or used to working longer hours or with greater physical effort than in other companies or countries or if they can be forced to do so. Similarly, a company can achieve effectiveness, for example large production numbers, through inefficient processes if it can afford to use more energy per product, for example if energy prices or labor costs or both are lower than for its competitors.
For example, one may measure how directly two objects are communicating: downloading music directly from a computer to a mobile device is more efficient than using a mobile device's microphone to record music sounds that come from a computer's speakers.
Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output ("product") produced per the amount C ("cost") of resources consumed. This may correspond to a percentage if products and consumables are quantified in compatible units, and if consumables are transformed into products via a conservative process. For example, in the analysis of the energy conversion efficiency of heat engines in thermodynamics, the product P may be the amount of useful work output, while the consumable C is the amount of high-temperature heat input. Due to the conservation of energy, P can never be greater than C, and so the efficiency r is never greater than 100% (and in fact must be even less at finite temperatures).