Koomey's law

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Computations per kWh, from 1946 to 2009

Koomey's law describes a long-term trend in the history of computing hardware. The number of computations per joule of energy dissipated has been doubling approximately every 1.57 years. This trend has been remarkably stable since the 1950s (R2 of over 98%) and has been somewhat faster than Moore's law. Jonathan Koomey articulated the trend as follows: "at a fixed computing load, the amount of battery you need will fall by a factor of two every year and a half."[1]

In 2011, Koomey re-examined this data[2] and found that 'Koomey's Law' had slowed. From 2000 the doubling period had slowed to every 2.6 years, instead of every 1.57 years. Koomey explains: "The difference between these two growth rates is substantial. A doubling every year and a half results in a 100-fold increase in efficiency every decade. A doubling every two and a half years yields just a 16-fold increase[3]."

This slowing is related to the end of Dennard scaling, which tracked the increasing efficiency of electronics with smaller sizes (Dennard's scaling ended in about 2005) and the slowing[4] of Moore's Law, which tracks the decreasing size of electronic components with time.


The implications of Koomey's law are that the amount of battery needed for a fixed computing load will fall by a factor of 100 every decade.[5] As computing devices become smaller and more mobile, this trend may be even more important than improvements in raw processing power for many applications. Furthermore, energy costs are becoming an increasing factor in the economics of data centers, further increasing the importance of Koomey's law.

The slowing of Koomey's Law has implications for energy use in information and communications technology. However, because computers do not run at peak output continuously, the effect of this slowing may not be seen for a decade or more[6]. Koomey writes that "as with any exponential trend, this one will eventually end...in a decade or so, energy use will once again be dominated by the power consumed when a computer is active. And that active power will still be hostage to the physics behind the slowdown in Moore’s Law.".


Koomey was the lead author of the article in IEEE Annals of the History of Computing that first documented the trend.[1] At about the same time, Koomey published a short piece about it in IEEE Spectrum.[7]

It was further discussed in MIT Technology Review,[8] and in a post by Erik Brynjolfsson on the “Economics of Information” blog,[5] and at The Economist online.[9]

The trend was previously known for digital signal processors, and it was then named "Gene's law". The name came from Gene Frantz, an electrical engineer at Texas Instruments. Frantz had documented that power dissipation in DSPs had been reduced by half every 18 months, over a 25 year period.[10][11]

Slowing and end of Koomey's law[edit]

Latest studies indicate that Koomey's Law has slowed to doubling every 2.6 years[12].

By the second law of thermodynamics and Landauer's principle, irreversible computing cannot continue to be made more energy efficient forever. As of 2011, computers have a computing efficiency of about 0.00001%.[13] Assuming that the energy efficiency of computing will continue to double every 1.57 years, the Landauer bound will be reached in 2048. Thus, after about 2048, Koomey's law can no longer hold.

Landauer's principle, however, is not applicable to reversible computing. This and other 'beyond CMOS' future computing technologies as-yet undeveloped would represent entirely new efficiencies, beyond Koomey's Law.

See also[edit]


  1. ^ a b Koomey, Jonathan; Berard, Stephen; Sanchez, Marla; Wong, Henry (29 March 2010), "Implications of Historical Trends in the Electrical Efficiency of Computing", IEEE Annals of the History of Computing, 33 (3): 46–54, doi:10.1109/MAHC.2010.28, ISSN 1058-6180.
  2. ^ http://www.koomey.com/post/153838038643
  3. ^ https://www.electronicdesign.com/microprocessors/energy-efficiency-computing-what-s-next
  4. ^ https://blogs.wsj.com/digits/2015/07/16/intel-rechisels-the-tablet-on-moores-law/
  5. ^ a b Brynjolfsson, Erik (12 September 2011). "Is Koomey's Law eclipsing Moore's Law?". Economics of Information Blog. MIT.
  6. ^ https://spectrum.ieee.org/computing/hardware/moores-law-might-be-slowing-down-but-not-energy-efficiency
  7. ^ Koomey, J. G. (26 February 2010), "Outperforming Moore's Law", IEEE Spectrum.
  8. ^ Greene, Kate (September 12, 2011). "A New and Improved Moore's Law". MIT Technology Review.
  9. ^ "Computing power—A deeper law than Moore's?". The Economist online. 10 October 2011.
  10. ^ Farncombe, Troy; Iniewski, Kris (2013), "§1.7.4 Power Dissipation", Medical Imaging: Technology and Applications, CRC Press, pp. 16–18, ISBN 978-1-4665-8263-7.
  11. ^ Frantz, G. (2000), "Digital signal processor trends" (PDF), IEEE Micro, 20 (6): 52–59, doi:10.1109/40.888703.
  12. ^ http://www.koomey.com/post/153838038643
  13. ^ Gualtieri, Dev (8 July 2011). "Landauer Limit". Tikalon Blog. Retrieved 2 July 2015.

Further reading[edit]