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Amdahl's law bounds the speedup obtained by accelerating only part of a fixed computation. Let fraction $s$ of its original execution time remain serial, while fraction $1-s$ divides perfectly among $p$ identical processors. ThenThe terms add because the serial and accelerated parts still both have to finish. If $s=0.1$, ten processors give $S_{10}=100/19\approx 5.26$; even infinitely many cannot exceed speedup ten.

Gene M. Amdahl's 1967 argument emphasized sequential work and irregularities in real computations.^[ref] The displayed idealized formula follows from the stated time decomposition. Communication, synchronization, unequal work and limited memory bandwidth can reduce actual speedup. Increasing the problem size changes the serial fraction and asks a different scaling question.

Gene M. Amdahl designed computer architectures and analyzed limits to speeding up computation by adding processors. His 1967 paper emphasizes sequential work and irregularities in real scientific programs rather than assuming every operation can be parallelized.^[ref]

In the standard idealized Amdahl's law model, a fixed workload with serial fraction $s$ and perfectly parallel remaining work has speedupIf $s=0.1$, ten processors give $S(10)\simeq 5.26$; even infinitely many processors cannot exceed a speedup of ten. Communication and synchronization can reduce the gain further. This bound fixes the original workload: scaling the problem along with the machine answers a different performance question.