Amdahl's Law Calculator
Calculate the theoretical speedup of a program using Amdahl's Law. Understand how parallelization affects performance based on the serial fraction of code.
Fraction of code that cannot be parallelized (0.0 to 1.0)
Number of processors or parallel units
How to Use This Calculator
- Enter the serial fraction (0.0 to 1.0) - the portion of code that cannot be parallelized.
- Enter the number of processors or parallel units (N).
- The calculator displays the theoretical maximum speedup and efficiency.
- Use this to understand parallelization limits and plan optimization strategies.
Amdahl's Law Formula
Amdahl's Law calculates theoretical speedup:
Where s = serial fraction (0-1), N = number of processors. Example: s = 0.1 (10% serial), N = 4 processors: Speedup = 1 / (0.1 + 0.9/4) = 1 / (0.1 + 0.225) = 1 / 0.325 = 3.08x. Maximum possible speedup (N → ∞) = 1/s = 10x.
Full Description
Amdahl's Law, formulated by Gene Amdahl in 1967, is a fundamental principle in parallel computing that predicts the theoretical maximum speedup achievable when parallelizing a program. It demonstrates that the serial (non-parallelizable) portion of code limits overall speedup, regardless of how many processors are available. This law is crucial for understanding the limits of parallelization and making informed decisions about hardware and software optimization.
The law shows that even with infinite processors, speedup is limited to 1/s, where s is the serial fraction. For example, if 10% of code is serial (s = 0.1), maximum speedup is 10x, no matter how many processors you add. This highlights the importance of minimizing serial code and optimizing the parallelizable portions. Amdahl's Law helps explain why some programs benefit greatly from parallelization while others show diminishing returns.
This calculator helps you understand Amdahl's Law by calculating theoretical speedup for different serial fractions and processor counts. Enter the serial fraction and number of processors, and it shows the speedup and efficiency. Use it to evaluate parallelization strategies, understand performance limits, or plan hardware investments. Amdahl's Law is essential knowledge for anyone working with parallel computing or high-performance systems.
Frequently Asked Questions
What is Amdahl's Law?
Amdahl's Law predicts the theoretical maximum speedup of a program when parallelizing part of it. It shows that the serial (non-parallelizable) portion limits the overall speedup, no matter how many processors you add.
What is the serial fraction?
The serial fraction (s) is the portion of code that cannot be parallelized, expressed as a decimal between 0 and 1. For example, if 10% of code is serial, s = 0.1. If 50% is serial, s = 0.5.
Why does speedup plateau?
As you add more processors, the parallel portion gets faster, but the serial portion remains constant. Eventually, the serial portion dominates, and adding more processors provides diminishing returns. This is why Amdahl's Law shows speedup approaching 1/s as N approaches infinity.
How do I determine the serial fraction?
Profile your code to identify serial sections (I/O, initialization, sequential algorithms). The serial fraction = (Time spent in serial code) / (Total execution time). For example, if serial code takes 1 second and total time is 10 seconds, s = 0.1.