Gmail Limits & the Population Bomb

Sometime yesterday, the UN officially declared the birth of the world’s 7 billionth baby. Once all the numbers were in, I couldn’t help wondering: how long do we have left before we out-birth GMail’s storage limit?

I didn’t know how quickly the world’s population is growing, so I asked Alpha:

1.21% / yr

Using a super-accurate stopwatch and the GMail homepage, I took down a couple values to approximate the current rate of expansion of GMail storage:

Time (seconds)Size (MB)
20 later7642.849572
If you buy those numbers—and there’s no reason why you should—GMail’s storage is currently expanding at a rate of about 4.5b/s, or roughly 142MB/yr.

Comparing the exponential growth (r1) of global population (C1) with the linear growth (r2) of the Gmail storage limit (C2), the number of years (n) before they meet is:

C1(1 + r1)^n = C2 + r2(n)

And the conclusion is:

Solving for n under the assumption that nothing will change, Gmail should be all set for at least the next 88 years.