Calculate Amdahl’s Law speedup, maximum speedup, or processors needed from the parallel portion and number of processors or cores.

Amdahl’s Law Calculator

Enter the parallel portion of your program and the processor count to get the expected speedup.

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Amdahl’s Law Formula

The following formula is used to calculate the speedup achieved by using parallel processing according to Amdahl’s Law:

Speedup = {1}/({(1 - p) + {p}/{n}})

Variables:

  • Speedup is the overall speedup achieved by parallel processing
  • p is the proportion of the program that can be parallelized (between 0 and 1)
  • n is the number of processors used (n ≥ 1)

To calculate the speedup, first compute the denominator (1 − p) + (p / n), then take its reciprocal: Speedup = 1 / ((1 − p) + (p / n)).

What is Amdahl’s Law?

Amdahl’s Law, named after computer architect Gene Amdahl, is a formula used to find the maximum improvement possible by enhancing a particular part of a system. In the context of parallel computing, it is used to predict the theoretical maximum speedup for program processing using multiple processors. The law states that the speedup of a program using a parallel algorithm is limited by the time needed for the sequential fraction of the program. In other words, if a program needs 20 hours to complete in sequential mode (i.e., with one processor) and a particular part of the program which takes one hour to execute cannot be parallelized, while the remaining 19 hours (95%) of execution time can be parallelized, then regardless of how many processors are devoted to a parallelized execution of this program, the minimum execution time cannot be less than that critical one hour. Hence, the speedup is limited by the non-parallelizable section of the process.

How to Calculate Amdahl’s Law?

The following steps outline how to calculate Amdahl’s Law:

  1. First, determine p, the fraction of total execution time that can be parallelized (0 to 1).
  2. Next, determine n, the number of processors (n ≥ 1).
  3. Next, compute the denominator: D = (1 − p) + (p / n).
  4. Next, compute the overall speedup: S = 1 / D.
  5. Finally, note that as n becomes very large (ideal scaling), the theoretical maximum speedup approaches Smax = 1 / (1 − p).

Example Problem : 

Using the following values, calculate the speedup S (using S = 1 / ((1 − p) + (p / n))).

number of processors used (n) = 4

proportion of the program that can be parallelized (p) = 0.6