Amdahl's Law Calculator — Parallel Speedup
Find out how much faster a program can run when parallelised, using Amdahl's Law. Enter the percentage of your program that can be parallelised and the number of processors, and see the speedup, maximum theoretical speedup, and parallel efficiency.
%
Factor by which execution time is reduced with the given number of processors
- 1
Serial fraction
s = 1 − 80% ÷ 100 = 0.2 - 2
Parallel-over-N term
p ÷ N = 0.8 ÷ 8 = 0.1 - 3
Denominator
s + p/N = 0.2 + 0.1 = 0.3Sum of the serial fraction plus the parallel work divided across all processors. - 4
Speedup
1 ÷ 0.3 = 3.33
How does this calculator work?
Amdahl's Law: S(N) = 1 / ((1−p) + p/N). If 80% of your program is parallelisable, the maximum possible speedup (with infinite processors) is 1/(1−0.8) = 5×. With 8 processors: S(8) = 1/(0.2 + 0.1) ≈ 3.3×. The serial fraction is the inescapable bottleneck — even 5% serial code limits maximum speedup to 20×.
Formula
How this is calculated
Amdahl's Law, formulated by Gene Amdahl in 1967, states that the maximum speedup achievable by parallelising a program is fundamentally limited by its irreducibly serial portion. If fraction p of the execution time can be parallelised perfectly across N processors, and fraction (1 − p) must run serially, then the total speedup relative to a single processor is S(N) = 1 / ((1 − p) + p/N).
As N grows towards infinity, the parallel term p/N shrinks to zero and the speedup converges to the maximum of 1/(1 − p). This is the key insight of Amdahl's Law: even 1% of serial code limits the maximum possible speedup to 100×, regardless of how many processors you add. A program that is 80% parallel has a ceiling of 5×; 90% parallel gives 10×.
Parallel efficiency measures how well the processors are used: efficiency = S(N)/N × 100%. It falls as N increases because the serial bottleneck becomes a larger fraction of total time. Gustafson's Law offers a complementary perspective — by scaling the problem size with N, the parallel fraction can grow and the serial portion shrinks relatively — but Amdahl's Law remains the baseline model for fixed-size workloads.
Frequently asked questions
It shows diminishing returns. Adding the 2nd processor often gives a near-2× speedup; adding the 1000th provides almost no gain if even a small fraction of the code is serial. The serial fraction acts as an absolute ceiling that no amount of parallelism can overcome.
Parallel efficiency is speedup divided by the number of processors (×100%). It starts near 100% for small N but falls as N grows, because the serial portion becomes an increasingly large share of total runtime. At the maximum speedup limit, adding more processors gives zero gain — efficiency approaches 0%.
Amdahl's Law assumes a fixed problem size: as you add processors, you reduce execution time. Gustafson's Law assumes you scale the problem size with N, keeping total runtime constant. In practice, large scientific workloads benefit from Gustafson scaling (larger problem = more parallelisable work), while Amdahl's Law is more relevant for latency-sensitive tasks.
TG we-Calculate Editorial Team. (2026). Amdahl's Law Calculator — Parallel Speedup [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/amdahls-law-calculator
TG we-Calculate Editorial Team. "Amdahl's Law Calculator — Parallel Speedup." TG we-Calculate. 2026. https://we-calculate.com/calculator/amdahls-law-calculator.
TG we-Calculate Editorial Team, "Amdahl's Law Calculator — Parallel Speedup," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/amdahls-law-calculator
@misc{wecalculate_amdahls_law_calculator, title = {Amdahl's Law Calculator — Parallel Speedup}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/amdahls-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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