I’ve always loved the verifiable, objective truth of math, and how math can help us understand our world. As a teenage girl, I particularly enjoyed statistics and game theory, at least at the level I could understand them (limited by my age!).
But I don’t like what that same math tells me now about transgender hair removal.
I wanted to know how long it would take for my facial hair to be removed. For a variety of reasons, I chose to do electrolysis and not laser, although I think most of this math also applies to laser removal.
At any point in time, about one third of your hair is in an active growth phase. For pretty much any hair removal technique, only the active hairs can be targeted for removal. With electrolysis, the hair is zapped and removed — so it has to be there for the zapping to take place. With laser, it has to be pigmented to absorb the energy. This is the first reason why all hair removal methods require more than one treatment.
The average hair cycle for the face is around nine months (some people have longer hair cycles). So this becomes the lower bound (least amount of time) for the length of time we have to do regular removal — an area of the face needs to be zapped multiple times during this nine months, regularly, to ensure that you get each hair as it wakes up.
In addition, once a hair is treated, it won’t regrow, even if the treatment was ineffective, until the next hair cycle. You get one shot per hair.
So how much hair can be removed in a growth cycle? A good electrologist can remove about 75% of the hair during this cycle, if they treat all areas routinely during the entire cycle. That means if you start with 10,000 hairs (a rough average), you’ll have 2,500 hairs at 9 months. That’s still a lot of hair. Too much for most trans women.
During the next 9 months, that good electrolysis will kill 75% of those 2,500 hairs. So at 18 months after starting, you’ll “only” have 625 hairs, but that’s probably more than most of us want.
How long to get down to say a dozen hairs, few enough that maybe you can just yank them out with tweezers when you see them?
I did the math.
It takes about 44 months of regular electrolysis.
How does this math work?
We start with a few known figures — 75% of hair is removed per cycle by a good electrolysis technician. We start with 10,000 hairs. And we are being optimistic and assuming a 9 month hair growth cycle. We’re also assuming every hair, when it is in its active state, will be treated during the cycle. That means each area of the face needs to be hit multiple times during that hair growth cycle.
First, though, how it doesn’t work
So, how much hair is removed in a month? You might think it’s 75% divided by 9, or 8.3%. But it’s not, it’s less than that. If you removed 8.3% of hair in one month, you would then have 91.7% of your hair left (100% minus 8.3% is 91.7%).
In month two, if you removed 8.3% of your hair, you would have 91.7% of 91.7% remaining:
.917 * .917 = 84% of hair remains
See the pattern? Month 1 is .917 raised to the power of 1 (.917¹). Month 2 is .917 raised to the power of 2 (.917²). So month 9 is .917 raised to the power of 9(.917⁹):
.917⁹ = 45.8% of hair remains
Wait! We know after 9 months, from our assumption about the work a good electrolysis technician can do, that you should lose 75% of your hair — so you’re left with 25%, not 59%!
So this isn’t how it works.
How the Math Really Works
Remember that pattern? We tried raising .917 to the power of 9 (.917⁹), and that didn’t work. But we actually know something here — we know:
x⁹ = .25 of hair remains
We just don’t know what x is (well, we don’t know the value of x, even though we do know that’s the amount, on average, of hair that remains after a month of treatment). Fortunately, with some pre-calculus math, we know that:
x⁹ = .25
Can be rewritten as
.25^(1/9) = x
That is, 25% raised to the power of one-ninth (this is also the 9th root of x). If you’re a bit rusty on this, or didn’t take pre-calculus, just trust me on this — we can solve the above and determine that for each month, you have about 86% of the hair that you had the previous month.
.25^(1/9) = .857
That is…after a month of treatment 85.7% of your hair will remain.
Now remember, most of this 85.7% of hair won’t be actively growing at that time — it’s either been temporarily removed (by being vaporized by the laser or pulled out by the electrologist) or the follicle was dormant (no hair) at the time. So your face might be hairless at this point, but 85.7% of the hair will come back.
We can check our math to see where we would be in nine months (remember, it should be 25% of hair remaining):
.857⁹ = .25 (yay!)
So, what does this mean in real life?
Scroll back up to to the chart I included — I put together an Excel spreadsheet to let you calculate this. To get down to a dozen or so hairs, at a 75% kill rate, a 9 month cycle, and starting with 10,000 hairs, it’ll take 44 months or so. That sucks.
What can make it take less time? Obviously if your technician was better at removing hair, it could be quicker. Let’s say xe can remove 80% of your hair per cycle (that would be really, really good — the best laser and electrology technicians claim 75–80%).
It still takes over 3 years to get to a dozen hairs — about 38 months. That’s 6 months better than the tech that does 75% effectiveness, which is good, but it’s not what any of us want to hear.
And what happens with a worse technician? How does that impact things?
Wow, at 4 years, you’re still stuck with nearly 250 hairs. That sucks.
So it’s worth finding a good tech!
But there’s another couple variables. What happens if you have a long hair growth cycle? Let’s say your hair growth cycle is 12 months long, not 9 months. Let’s go back to a good tech, someone who can kill 75% of them.
At four years, you still would have around 40 hairs left, which sucks.
How about the other variable? Let’s say you start with 15,000 hairs instead of the more typical 10,000. Let’s go back to our 75% kill rate tech, and let’s say you have the 9 month cycle time. Remember, when you started with 10,000 hairs, you got to a dozen hairs left at about 44 months. Where will this go?
Okay, you started with 50% more hair, but it only took a few more months to get down to a dozen hairs or less — 47 months from the start, or 3 months longer than the woman who started with only two thirds as much hair.
I don’t believe your assumptions! (or I’d like to play with the numbers myself!)
That’s fine, I’ve made the spreadsheet available for everyone to use (under the terms of the GNU Public License 3.0) — you can download the Excel spreadsheet here: https://github.com/jmaslak/hair-removal/blob/master/hair-removal-worksheet.xlsx?raw=true
What isn’t accounted for?
Repeat treatments may may it more likely that your hair is killed the second, third, or forth time it’s treated — not 75% likely to be killed, but maybe 85% or 95% or something else. Of course it’s also possible these hairs are particularly strong and nearly impossible to kill. I just don’t know. But even if their kill rate does increase, it still will take years to get the majority of hair killed.
What about surgical prep electrolysis?
That hair has a shorter cycle time. Still, it can take some time!
So, what can we conclude?
Hair removal sucks. It’s slow.
We also saw that a good tech may be worth the money — and a poor tech probably isn’t.
The amount of hair you start with isn’t as important as your hair cycle time. If you have a longer cycle time, it’s going to take you longer — and you can’t do anything about it.
What is important is getting to the state where you are treating all your face multiple times during a hair growth cycle. that will eventually eliminate the hair, but it’s a slow process.
I’ll also send virtual hugs to any other women who are highly dysphoric from their facial hair.