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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.

Parallel computing performs multiple parts of a computation simultaneously, typically on several processors or execution units. It requires decomposing work and coordinating data dependencies, communication and synchronization. Concurrent computing also permits overlapping activities on a single processor, so concurrency alone does not imply simultaneous hardware execution.

If fraction $s$ of a fixed computation remains serial and the rest divides perfectly among $p$ processors, the idealized runtime is $T_p=T_1(s+(1-s)/p)$. Thus Amdahl's law gives speedupfor $s>0$. With a 10 percent serial fraction and 10 processors, the ideal speedup is about 5.26, before communication overhead. The calculation assumes a fixed workload; changing the workload size changes the question. Load imbalance and limited memory bandwidth can further reduce the achieved gain.