Grosch's Law

Figure 3.2: Power-cost relationship according to Grosch's law.

• It was as early as the late 1940s that H. Grosch studied the relationship between the power of a computer system, $P$, and its cost, $C$.
• He postulated that $P=K*C^s$, where $s$ and $K$ are positive constants. Grosch postulated further that the value of $s$ would be close to 2. Simply stated, Grosch's law implies that the power of a computer system increases in proportion to the square of its cost (see Fig. 3.2).
• Alternatively, one can express the cost of a system as $C=sqrt(P/K)$ assuming that $s= 2$.
• According to Grosch's law, in order to sell a computer for twice as much, it must be four times as fast. Alternatively, to do a computation twice as cheaply, one has to do it four times slower. With the advances in computing, it is easy to see that Grosch's law is overturned, and it is possible to build faster and less expensive computers over time.