Amdahl's Law Calculator
Calculate theoretical speedup from Amdahl's law using parallelizable task proportion, speedup factor, and original execution time.
What Is Amdahl's Law?
Amdahl's law estimates the maximum speedup you can achieve by improving only part of a task. Even large speedups on a parallelizable fraction are limited by the sequential portion that cannot be sped up.
Amdahl's Law Formula
$$S = \frac{1}{1 - p + \frac{p}{s}}$$ $$T_{new} = \frac{T_{old}}{S}$$Where \(p\) is the parallelizable fraction, \(s\) is the speedup factor applied to that fraction, and \(S\) is the overall speedup.
Maximum Possible Speedup
$$S_{max} = \frac{1}{1 - p}$$Related tools: Productivity Calculator and Binary Calculator.
Frequently Asked Questions
Why does speedup plateau even with many processors?
The sequential fraction sets a hard ceiling. If 30% of the task cannot be parallelized, speedup cannot exceed about 3.33× no matter how many cores you add.
What should p represent?
p is the fraction of total execution time that benefits from parallelization or other performance improvements.
Does this predict real-world performance exactly?
No. It is a theoretical upper bound. Memory, I/O, and coordination overhead can reduce actual gains.
When should I use Amdahl's law?
Use it when deciding whether investing in parallel hardware or optimizing a hot code path is worth the cost.
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