Amdahl’s Law Calculator
Amdahl’s law limits speedup by the part you cannot improve: speeding up 80 % of a program 8× gives only 3.333333333 overall.
3.33333333333333
Full answer, then cut to fewer decimals (not rounded):
- 3.33333333333333
- 3.3333333333333
- 3.333333333333
- 3.33333333333
- 3.3333333333
- 3.333333333
- 3.33333333
- 3.3333333
- 3.333333
- 3.33333
- 3.3333
- 3.333
- 3.33
- 3.3
- Maximum speedup as s → ∞, 1/(1 − p)
- 5
- Parallel efficiency S ÷ s
- 0.4166666667
- New time as a share of the old
- 30 %
Step-by-step solution
- S = 1 ÷ [(1 − p) + p/s]
- = 1 ÷ [0.2 + 0.8/8] = 3.333333333
Amdahl’s Law Formula
S = 1 ÷ [(1 − p) + p/s]
p fraction improved, s its speedup; limit 1/(1 − p)
Worked Example
80 % of a program made 8 times faster:
- S = 1 ÷ [(1 − p) + p/s]
- = 1 ÷ [0.2 + 0.8/8] = 3.333333333
Parallel efficiency S ÷ s: 0.4166666667 · New time as a share of the old: 30 %
GATE tip
If a question gives the overall speedup and asks for the fraction, rearrange: p = (1 − 1/S) ÷ (1 − 1/s).
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Frequently asked questions
What is the maximum speedup by Amdahl’s law?
1/(1 − p), however fast the improved part becomes: with 80 % parallel code, at most 5×.
How is Gustafson’s law different?
Gustafson assumes the problem grows with the processors, giving scaled speedup (1 − p) + p·N, which is more optimistic.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Amdahl’s Law Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/amdahls-law-calculator/
IEEE
Scientific Converters, "Amdahl’s Law Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/amdahls-law-calculator/