Amdahl's Law Calculator
The speedup a parallel program gets from more processors when part of it must run serially — Amdahl's law — with the ceiling that serial fraction imposes, the efficiency per processor, and Gustafson's scaled alternative.
If a tenth of a program cannot be parallelised, no number of processors makes it more than ten times faster.
How the amdahl's law calculator works
If a tenth of a program cannot be parallelised, no number of processors makes it more than ten times faster. Amdahl's law puts a number on it: speedup is one over the serial fraction plus the parallel fraction divided by the processor count. The efficiency — speedup per processor — falls steadily, which is why doubling the cluster rarely halves the time.
Gustafson's law looks at it the other way: with more processors you solve a bigger problem in the same time, and the serial fraction matters less.
Formula: S(n) = 1 / ((1 − p) + p/n); S_max = 1 / (1 − p); Gustafson: S = (1 − p) + p n
Worked examples
| Inputs | Speedup | Note |
|---|---|---|
| 90% parallel on 16 processors | 6.4 | 6.4× of a possible 10 |
| A serial bottleneck | 1.8824 | never above 2× |
| Nearly all parallel | 72.1127 | still only 72× |
FAQFrequently asked questions
What is Amdahl's law?
The speedup of a program from parallelism is limited by the part that stays serial. With 10% serial, the ceiling is 10× however many processors you add.
Why does efficiency fall?
Because the serial part takes the same time regardless, so each added processor contributes less. At 90% parallel, 16 processors are 40% efficient; 256 are under 4%.
What is Gustafson's law?
The observation that people use more processors to solve bigger problems in the same time, not the same problem faster. Then speedup grows linearly, because the serial share shrinks relative to the work.
How do I find the parallel fraction?
Profile: the time in phases that are single-threaded — I/O, setup, reductions, synchronisation — is the serial part. Or fit the law to timings at two processor counts.
Does this include communication overhead?
No — the law assumes the parallel part scales perfectly. Communication makes real scaling worse than Amdahl, never better.
Where these figures come from
- IEC 80000-13 — Information science and technology (quantities and units) — the decimal (kB, MB) versus binary (KiB, MiB) prefixes used throughout
- RFC 4632 — Classless Inter-domain Routing (CIDR) — the address-plan arithmetic behind the subnet calculator
- RFC 1918 — Address Allocation for Private Internets — the private ranges the subnet calculator recognises
- NIST SP 800-63B — Digital Identity Guidelines, Authentication — length over composition rules; the basis of the password guidance here
- NIST SP 800-57 Part 1 — Recommendation for Key Management — key-strength comparisons used by the key-space calculator
- Australian Cyber Security Centre — Essential Eight — national guidance on passphrases and system hardening
Last checked: September 2026. Units follow the SI decimal convention (IEC 80000-13 defines the binary alternatives); network and security figures cite the defining standard.