Amdahl's law, also known as Amdahl's argument, is named after computer architect Gene Amdahl, and is used to find the maximum expected improvement to an overall system when only part of the system is improved. It is often used in parallel computing to predict the theoretical maximum speedup using multiple processors.

The speedup of a program using multiple processors in parallel computing is limited by the time needed for the sequential fraction of the program. For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours (95%) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour. Hence the speed up is limited up to 20×, as the diagram illustrates.

Recently, Amdahl's law has begun to draw skepticism.  In a paper published by John L. Gustafson which states:

At Sandia National Laboratories, we are currently engaged in research involving massively-parallel processing. There is considerable skepticism regarding the viability of massive parallelism; the skepticism centers around Amdahl's law, an argument put forth by Gene Amdahl in 1967 [1] that even when the fraction of serial work in a given problem is small, say s, the maximum speedup obtainable from even an infinite number of parallel processors is only 1/s. We now have timing results for a 1024-processor system that demonstrate that the assumptions underlying Amdahl's 1967 argument are inappropriate for the current approach to massive ensemble parallelism. (read more)