Table of Contents

Amdahl's law

Amdahl's law quantifies the maximum speedup from parallelization given a fixed problem size: if fraction $p$ is parallelizable and $(1-p)$ is sequential, maximum speedup is $S_{\max} = \frac{1}{1-p}$. The sequential fraction acts as a hard ceiling—adding more cores beyond a point yields diminishing returns.

For 90% parallelizable code, max speedup is 10×; for 99%, it's 100×. Finding and eliminating sequential bottlenecks is often more effective than adding cores.

Example

This table shows how the sequential fraction limits speedup.

Parallel fraction (p)  Maximum speedup
50%                   2×
75%                   4×
90%                   10×
95%                   20×
99%                   100×