How many times more powerful is a modern phone than the Apollo 11 computer?

How to get close to this number

Divide the clock speeds and then some. The explanation gives the historic machine at 0.043 megahertz with four kilobytes of memory; a modern phone runs at thousands of megahertz across multiple cores with millions of times the memory. The ratio comes out in the tens of thousands to millions depending on which measure you use.

Which measure matters, and it is worth naming: clock speed, memory, instructions per second and total transistor count all give different ratios. A single "times more powerful" figure is a simplification of several comparisons that do not agree, which is why published versions of this statistic vary by orders of magnitude.

The framing in the explanation is the one that lands regardless: that machine landed people on the Moon, and a phone uses more computing power to autocorrect a message. The point is not that phones are impressive but that the Moon landing required far less computation than people assume — most of the problem was solved with slide rules, wind tunnels and engineering judgement.