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.
This table shows how the sequential fraction limits speedup.
Parallel fraction (p) Maximum speedup 50% 2× 75% 4× 90% 10× 95% 20× 99% 100×