How to use Amdahl's law
Enter the percentage of the original single-processor runtime that can be divided among processors. Then enter the processor or worker count and a positive baseline runtime. The runtime unit is only a label; use the same unit when interpreting the projected result.
This tool models a fixed amount of work. It does not benchmark your computer, inspect code, or discover the parallel fraction. Estimate that fraction from profiling or a defensible workload breakdown.
- Enter the parallelizable portion from 0% through 100%.
- Enter a whole processor count of at least one.
- Enter the one-processor baseline runtime and choose seconds, minutes, or hours.
- Calculate the ideal speedup, efficiency, projected runtime, saved time, serial share, and asymptotic ceiling.
Formula and interpretation
For parallel fraction P and N processors, relative runtime is (1 − P) + P/N. Speedup is 1 divided by that relative runtime. Efficiency is speedup divided by N. Projected runtime is baseline runtime multiplied by relative runtime.
The serial fraction 1 − P limits the result. As N approaches infinity, the ideal speedup approaches 1/(1 − P). When P is exactly 100%, this simplified ceiling is unlimited, but real machines still have overhead and finite resources.
Worked examples
90% parallel on eight processors
Relative runtime is 0.10 + 0.90/8 = 0.2125. Speedup is about 4.71× and efficiency about 58.82%. A 100-second baseline becomes 21.25 seconds, saving 78.75 seconds.
50% parallel on four processors
Relative runtime is 0.50 + 0.50/4 = 0.625. Speedup is 1.6× and efficiency is 40%. The infinite-processor ceiling is only 2×.
Why processor count has diminishing returns
Adding processors shrinks only P/N; it does not shrink the serial portion. Once the parallel term becomes small beside the serial term, each additional processor changes total time very little. Efficiency therefore usually falls as processors are added in this ideal fixed-work model.
Use the output as a selection aid: compare plausible processor counts and ask whether the smaller projected runtime justifies the added resources. It is a theoretical upper-style estimate, not a promise of measured performance.
Assumptions and limits
- The workload size and parallel fraction stay fixed.
- Parallel work divides perfectly and processors have equal performance.
- Communication, synchronization, scheduling, memory bandwidth, cache effects, startup, contention, and load imbalance are treated as zero.
- The baseline represents the same work and implementation.
- Real runtime may be slower and can even worsen when overhead dominates.
Frequently asked questions
Is the parallel percentage CPU utilization?
No. It is the share of original runtime that can be accelerated in parallel.
Why is eight processors not an 8× speedup?
Any serial work remains, and even this ideal model cannot divide it.
What does efficiency mean?
Speedup divided by processor count, shown as a percentage of ideal linear scaling.
Does the model include overhead?
No. The note deliberately states that overhead is excluded.
When should I benchmark?
Always before making a consequential capacity or hardware decision; use this model to frame expectations.