Does it take two weeks for a single man to produce enough sperm to impregnate every fertile woman on Earth?

Question

Fact Slides has a slide that claims:

A single human male produces enough sperm in two weeks to impregnate every fertile woman on the planet.

It sources a book of random facts

Is it true?

Answer 1

Theoretically that is rough-ballpark-correct. But that is assuming that you would need only one sperm per woman, which is unrealistic.

Using the... erm... "normal" way, not every sperm finds its way to the ovum, if there is a (fertile) ovum to be found. That is why males produce so many of them. It's a shotgun approach by evolution; the most mobile, healthiest sperm has the highest chance to "get there" first.

In-vitro fertilization does not have a 100% "hit rate" either; actually quite far from it.

Then there is the issue of how many woman on earth are fertile in the first place, and getting a number of those would include a lot of guesswork as well.

Which reduces the question to a more theoretical, "how long does an average male take to produce as many sperms as there are women on Earth".

We have somewhere between 7 and 8 billion people on earth, so very roughly speaking 4 billion women. (For a more detailed cracking down on that number, check fyrepenguin's answer.)

How many sperms a man produces per day is of course also just a ballpark figure. Two sources I found ad hoc:

• 290 million per day
• 1500 per second (amounting to 129.6 million per day)

So for 4 billion sperms, that would be 13.8 to 30.9 days, given these numbers.

Answer 2

Based on some information in the answer by DevSolar I will estimate the number of sperm in the range of 190-290 million a day, which as noted has a fair amount of uncertainty. However, I'm willing to do a little back-of-the-envelope guesswork to refine the estimate regarding the number of fertile women.

Currently, there are approximately 7.7 billion people in the world, and using information from this population pyramid (seen below) we can get a better estimate for the number of fertile women than just taking half that number.

I will be using 15-50 as the fertile age range (give or take) and that brings us to a more reasonable 1.91 billion women in that age bracket. With our estimate of 1.9 billion fertile women, that brings us to between 6.5-14.7 days, depending on your which estimate of sperm production rate. The upper end of which is pretty much exactly 2 weeks.

However (as DevSolar notes), that's assuming that all 1.9 billion sperm are both viable and able to be separated out individually and used as such, which is not how artificial insemination currently works.

If you want to quibble over the exact limits of what I used, you can redo the calculations with whatever limits you want off of the data below. Also, in the USA, infertility in women is around 10% or so, and there's definitely a more in-depth analysis that could be done using more detailed charts of infertility as age increases, so the numbers I've used are probably on the side of overestimation regarding the number of fertile women worldwide.