Gustafson's Law Speedup Calculator
Gustafson's Law is the optimistic counterpart to Amdahl's Law. Instead of asking how much faster a fixed task runs, it asks how much more work a larger machine can do in the same time, which matches how high-performance computing is used in practice. Because the parallel work scales with the processor count while the serial work stays roughly fixed, speedup rises almost linearly rather than hitting a ceiling. This calculator takes your parallel fraction and processor count, applies the Gustafson scaled-speedup formula, and reports speedup and parallel efficiency. The parallel fraction is workload-specific, so it is your input.
Gustafson's Law formula
P = parallel fraction (0 to 1), N = processors
Scaled speedup S = N - (1 - P) * (N - 1)
Equivalent: S = (1 - P) + P * N
Efficiency = S / N
Loss vs. linear = N - S
The two forms are algebraically identical. Speedup rises roughly linearly with N, offset only by the constant serial share, so larger machines keep paying off rather than saturating.
Scaled-speedup context
- Gustafson models weak scaling: the problem grows to fill the machine, holding wall-clock time roughly constant.
- Speedup is unbounded in N for any P greater than 0, unlike the Amdahl ceiling.
- At P = 1 the speedup equals N exactly, which is perfect linear scaling.
- The serial fraction lowers the slope of the speedup line but never caps it.
- Real systems still lose performance to communication and load imbalance not captured by the basic law.
Gustafson's Law: frequently asked questions
What is Gustafson's Law?
Gustafson's Law gives the scaled speedup of a parallel workload that grows with the resources available. Speedup S equals N minus (1 minus P) times (N minus 1), where N is the processor count and P is the parallel fraction. It models the common case where larger machines are used to solve larger problems in the same time.
How does it differ from Amdahl's Law?
Amdahl fixes the problem size and finds a speedup ceiling, which is pessimistic. Gustafson scales the problem with the processors and gives near-linear speedup. Both are correct for their assumptions: use Amdahl when the workload is fixed, Gustafson when you scale the workload up to fill a bigger machine.
What is the parallel fraction here?
P is the fraction of the scaled workload that runs in parallel, between 0 and 1. In Gustafson's framing this fraction is measured on the parallel system at its full problem size, not on a single processor. It is a property of your workload, entered as an input.
Why is Gustafson speedup close to linear?
Because the serial work stays roughly constant while the parallel work grows with the machine, the serial portion becomes a smaller share of a larger total. The speedup formula therefore rises almost linearly with processor count, avoiding the hard ceiling that Amdahl's Law imposes.
What is the serial fraction's effect?
The serial fraction (1 minus P) is the penalty term: each additional processor adds nearly one unit of speedup minus that serial share. A larger serial fraction lowers the slope of the speedup line but does not cap it, which is the key practical difference from Amdahl's Law.
Official sources
- NIST: Engineering Statistics Handbook for the underlying linear 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.