Amdahl's Law Speedup Calculator
Amdahl's Law answers a hard question in parallel computing: if part of a task can be sped up but part cannot, how much faster does the whole task run as you add processors? Because the serial portion never shrinks, speedup hits a ceiling no matter how many cores you throw at it. This calculator takes the parallel fraction of your workload and a processor count, applies the closed-form Amdahl speedup, and also reports the theoretical maximum speedup as processors tend to infinity, plus the parallel efficiency. Estimating the parallel fraction is workload-specific, so it is your input.
Amdahl's Law formula
P = parallel fraction (0 to 1), N = processors
Speedup S = 1 / ((1 - P) + P / N)
Max speedup = 1 / (1 - P) as N to infinity
Efficiency = S / N
Serial fraction = 1 - P
The denominator is the serial part plus the parallel part divided across N processors. As N grows, the P/N term vanishes and speedup approaches the ceiling 1/(1 - P).
Parallel computing context
- The serial fraction sets a hard ceiling: 90 percent parallel caps speedup at 10 times regardless of processor count.
- Efficiency falls as N rises because the serial work does not shrink with more processors.
- Amdahl assumes a fixed problem size; for scaled problems use Gustafson's Law instead.
- Small reductions in the serial fraction can raise the ceiling sharply: 99 percent parallel allows 100 times.
- Real systems also lose time to communication and synchronisation overhead not modelled by the basic law.
Amdahl's Law: frequently asked questions
What is Amdahl's Law?
Amdahl's Law gives the theoretical speedup of a fixed-size task when part of it is parallelised. Speedup S equals 1 divided by ((1 minus P) plus P over N), where P is the parallel fraction and N is the number of processors. It captures the fact that the serial portion limits how much faster the whole task can run.
What is the maximum possible speedup?
As the processor count tends to infinity, Amdahl's Law gives a hard ceiling of 1 divided by (1 minus P). If 90 percent of the work is parallel, the maximum speedup is 10 times no matter how many processors you add. The serial 10 percent is the bottleneck. This calculator reports that ceiling.
What is the parallel fraction P?
P is the proportion of the task's runtime that can be executed in parallel, expressed between 0 and 1 (or as a percentage here). The remaining fraction, 1 minus P, must run serially. Estimating P accurately is the hard part; it is a property of your specific workload and is entered as an input.
How does Amdahl differ from Gustafson's Law?
Amdahl assumes a fixed problem size and asks how much faster it runs with more processors, yielding a speedup ceiling. Gustafson's Law assumes the problem grows with the processors available and gives a more optimistic, linear scaling. The two answer different questions; use Amdahl for fixed workloads.
What is parallel efficiency?
Parallel efficiency is the speedup divided by the number of processors, often shown as a percentage. An efficiency of 1 (100 percent) means perfect linear scaling. Efficiency falls as you add processors because the serial fraction does not shrink, so each added processor contributes less.
Official sources
- NIST: Engineering Statistics Handbook for the underlying ratio mathematics.
- NIST: National Institute of Standards and Technology reference root.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.