Amdahl’s Law, explained.
Amdahl's Law describes the limit on speeding up a fixed task when only part of the work can run in parallel.
Why it happens
Workers can share the parallel portion, but the serial portion still takes its original time. As more workers are added, the serial work becomes the bottleneck. The formula assumes perfect sharing and excludes extra coordination overhead.
Speeding up one part of a job leaves the untouched part as a bottleneck.
Read the result
Increase worker count while holding the parallel fraction fixed. Notice the diminishing improvement and compare it with the ceiling set by the serial fraction.
A worked example
Four workers on a partly shared job
A task takes ten hours: two hours must happen serially and eight can be divided perfectly.
With four workers, parallel work takes two hours, so the whole job takes four hours: a 2.5× speedup.
Even infinitely many workers cannot remove the two serial hours. The ideal maximum speedup is 5×.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Speedup with n processors is 1/[(1−p)+p/n], where p is the parallelizable share. The plot shows speedup for 1–32 processors at the selected share.
Where this idea is useful
A practical use
Estimate whether parallelizing a slow data task will justify more servers.
A common misconception
“Twice as many workers always finish twice as fast.”
Serial work and coordination can limit the improvement. The simple model already has a ceiling before overhead is added.
What this explanation leaves out
- Coordination overhead and changing workload are excluded, so real gains can be smaller.
What if the workload grows with the team?
That is a different scaling question. Amdahl's fixed-workload comparison does not automatically describe larger problems enabled by more resources.
Which part of your process must finish before other work can proceed?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.