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

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?

• Any chance of some answers that aren't prohibited back-of-the-envelope calculations? Jun 12 '20 at 23:10

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:

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

• The claim is fertile women, not all women. Jun 12 '20 at 5:58
• @Oddthinking And I refuse to engage in guesswork on how many are. The uncertainty in how many sperms your average male produces dwarfs that uncertainty anyway. But I rephrased a bit. Jun 12 '20 at 6:00
• @DevSolar I was willing to engage in that guesswork, though I agree that the uncertainty on the male side of the equation is significant. Jun 12 '20 at 9:15
• Even if every sperm would be able to find it's way to the ovum, a single sperm can't impegrate it. Jun 12 '20 at 18:22
• @AsteroidsWithWings: The number could be a bit misleading, That is not the same 1500 completed from scratch. The biological process for each cell takes around two months (ref: pubmed.ncbi.nlm.nih.gov/7972051 ). However, the throughput is 1500 per second because billions are being produced in parallel. Jun 12 '20 at 23:05

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.

• Nice work. Though it should be noted that the ratio fertile women / total women will always be <1, so this just makes an answer of "quite plausible" even more plausible. For appropriate definitions of "plausible". ;-) Jun 12 '20 at 9:26
• @DevSolar Agreed. It just bothered me slightly that you'd gone through effort to locate numbers for one side, then opted for an "ehhh, 50% of the population" approach, and I figured that it would be interesting enough information. Not casting any aspersions on your answer though; I've used your numbers in my calculations, and agree with what you've written there. I just wanted this as supplemental information for anyone like me who was interested in a more accurate estimation about the number of women Jun 12 '20 at 20:13
• @DevSolar What I would be interested in seeing would be taking the numbers in this chart, and multiplying them by (1- %sterile) by age, as well as a % menstruating by age. That way you would account for the majority of factors in estimating the number of fertile women in the world, and not use arbitrary estimated limits as I did here. I'd also be curious if there was any information about sperm production rate as it relates to age, possibly including some sort of variance as well in the chart. Jun 12 '20 at 20:16