Amdahl's Law Calculator (Parallel Speed-up Limit)
Speed-up of a program on n processors from the share that can run in parallel, the ceiling it can never pass, and how efficiently the cores are used.
Results
The dashed line marks the value you entered.
What this tool does
Amdahl's law says the part that must run serially sets a hard ceiling: if 10 % of the work cannot be parallelised, no number of cores will ever give more than 10 times the speed. With 90 % parallel work, 8 cores give only 4.7 times, and 64 cores 8.8 times, so efficiency drops quickly. The law assumes a fixed problem size and no overhead; real programs also pay for communication and waiting, so measured speed-ups are lower, while Gustafson's law points out that bigger machines are often used for bigger problems.
Formula
speed-up = 1 ÷ ((1 − p) + p ÷ n) · limit as n → ∞ = 1 ÷ (1 − p)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p | Share of the work that can run in parallel | % |
n | Number of processors (or cores) | — |
SP | Speed-up | × |
MX | Maximum speed-up with unlimited processors (0 = no limit) | × |
EF | Efficiency (speed-up ÷ processors) | % |
Worked example
- Share of the work that can run in parallel90 %
- Number of processors (or cores)8
- Speed-up4.71 ×
- Maximum speed-up with unlimited processors (0 = no limit)10.00 ×
- Efficiency (speed-up ÷ processors)58.8 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.