The formula
factor = 2 raised to (months in the span ÷ months per doubling)
Where it comes from
Gordon Moore observed in 1965 that the number of transistors per chip was doubling every year, and he himself revised that to two years in 1975. The "eighteen months" everybody repeats he never said: it is a version that circulated afterwards and stuck. What is interesting about the law is not the particular figure but the shape: anything doubling at regular intervals grows in a way intuition does not follow. Ten years doubling every two is 32 times more, not 5.
How to work it out by hand
- Convert the span to months
- Divide by the months per doubling
- That is how many doublings fit in the span
- Raise two to that number
What is worth knowing
Moore’s law as an observation about transistors has been slowing for some time: process nodes no longer shrink at the old rate and cost per transistor stopped falling around 28 nanometres, so the economic half of the original statement no longer holds. What does keep growing fast is performance by other routes: more cores, specialised accelerators and different memory architectures. And the exponential shape keeps turning up where intuition fails just as badly: compound interest, an epidemic in its early phase, or the cost of training a model. That is why this calculator takes any doubling period and any starting value: the law is a template, not a physical constant.