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).
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 does not 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. In some cases efficiency can be indirectly quantified with a non-percentage value, e.g. 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.