Universal Scalability Law Calculator
How to use Universal Scalability Law Calculator?

Measure the throughput and the number of servers to understand how it will perform when scaling up.

Giving N as the number of concurrency, servers, or processors.

C(N) as the relative capacity, throughput, or tasks per second.

Click CALCULATE button to fit the α and β parameters.

Recommend providing at least 4 sampling data for better estimations.

The fitting algorithm is Levenberg–Marquardt from ml-levenberg-marquardt library.

What is The Universal Scalability Law?

The Universal Scalability Law (USL) is a model used to evaluate the performance of parallel systems under increasing load, particularly when discussing computer servers or databases.

While Amdahl’s Law states the theoretical maximum speedup achievable due to parallel processing, the USL goes one step further and characterizes the behavior of scalability in realistic systems, considering the overheads that arise when multiple tasks are executed in parallel.

The Universal Scalability Law Formula

C(N)=N1+α(N1)+βN(N1)C(N) = \frac{N}{1 + \alpha(N-1) + \beta N(N-1)}


  • C(N) is the relative capacity of a system (which can be performance or throughput) as a function of the number of processing elements N.
  • α is the contention parameter (which represents serialized or linear component of the workload).
  • β is the coherency factor (which measures the influences from the overhead introduced by crosstalk between parallel executing tasks).

Key takeaways from USL:

  1. USL accounts for two primary facets that impede scalability: serialization (from Amdahl’s Law) and crosstalk or coordination penalty (the overhead introduced when tasks communicate with each other).
  2. Unlike Amdahl’s Law, which gives an optimistic representation, USL provides a more realistic picture of scalability by incorporating these penalties of parallel processing.
  3. USL is useful for modeling, predicting, and understanding the performance scalability of systems, which can help guide decisions about system design and capacity planning.