Does Anyone Remember the Terminal Length Formula?

[Naluin]

On the old boards, there was a thread in which someone had posted a formula for determining theoretical terminal length using the following information:

I = Number of individual hairs
S = Number of hairs shed daily
G =Monthly growth rate

The idea, IIRC, was that knowing one's daily shed rate and approximately how many hairs were on the head allowed one to estimate the lifespan of the hair follicles. Then one multiplied that lifespan in months by the monthly growth rate to get a theoretical terminal length.

Does any remember the original formula or have links that might be related? My own attempts at figuring out my theoretical terminal length gave me over seven feet of hair, so I have doubts about my rendition of this formula.

My rendition, for the record: (12*I*G)/(365*S)

[jojo]

oh i remember this the golden ratio i think it was called, hope somebody posts!

[TammySue]

There was a formula that you plugged in the numbers and it calculated your terminal length! Maybe someone can find it for us. :)

[eadwine]

That one where you plugged in numbers had a terminal length SHORTER than what I have now.. :lol: Not reliable ;)

I remember one where one of our members had calculated things, that one came out pretty decent and feasible. Can't remember who that was now.

[EdG]

I think that formula is right. It checks out dimensionally and gives a result in inches (for a monthly growth rate in inches).

length = (12 months/year * hairs * inches/month) / (365 days/year * hairs/day)
length = inches

I interpret the result not so much as a hard limit, but rather as a "length constant" which describes the rate of taper. Modeling hair taper as an exponential decay, 37% of one's hairs can be expected to reach the length given by the formula.

I think hair taper is pretty complicated, being determined by both the growth cycle and random breakage. I also notice that terminal length is different on different parts of the scalp. :)
Ed

[Naluin]

I interpret the result not so much as a hard limit, but rather as a "length constant" which describes the rate of taper. Modeling hair taper as an exponential decay, 37% of one's hairs can be expected to reach the length given by the formula.

I think hair taper is pretty complicated, being determined by both the growth cycle and random breakage. I also notice that terminal length is different on different parts of the scalp. :)
Ed

37%, huh? That's more than I would have expected, actually.

[EdG]

37%, huh? That's more than I would have expected, actually.I'm assuming an exponential decay

n=exp (-length/length_constant)

where length_constant is given by (12*I*G)/(365*S) as Naluin said.

exp (-1) is 37%.

I have some graphs on my website illustrating this http://www.edgrochowski.com/haircare.htm

Hope this helps. :)
Ed

[Nevermore]

I'm horrible at math. Just horrible. Would someone who isn't horrible at it do my formula for me?

[Patrycja]

owwwwwwwww my head hurts LOL

I'm going to take the easy way out and just wing it.When my hair stops growing after all I've done to speed it along(short of a major cut)that's when I know I've reached terminal.

Or at least a slowing down point.

[EdG]

I'm going to take the easy way out and just wing it.When my hair stops growing after all I've done to speed it along(short of a major cut)that's when I know I've reached terminal.That's a good approach. :)

The mathematical model is too simple to produce an accurate answer. Growing one's hair will give the right answer. :D
Ed

[Cinnamon Hair]

Hair Growth Calculator by Neil (http://www.allvidzhaze.com/phptest/hairgrowth.html)

Divine Proportion -- Golden Ratio (http://goldennumber.net/body.htm)

[Naluin]

EdG, I've been to your site before. :) When I was trying to find a terminal length formula on the web, Google had your site listed among the top results. I recognized your picture immediately, but only skimmed the graphs.

Now that I look at them more closely, they do make sense.

ilovemycop, I'm sorry we hurt your head. My nerd is showing a bit, I'm afraid. :flower:

[Igor]

I calculated mine like this:

Number of follicles on your head / (Average shedded hairs per day x 365)= the number of years it will take your scalp to “run out of” hairs at the maximum length

Previous number x 12 x your average month growth rate (Or just x your average yearly growth rate)¨

Edit: Of course this doesn’t change the fact that some follicles have a longer growth faze than other

[Patrycja]

hehe its ok.Anything with math makes my brain scream,I'm afraid.

[Rebelkat]

Hmmm... interesting. According to EdG's formula and calculating by 50 hairs lost per day (I actually think I'm losing less than that, but just to be safe...), I should be able to reach my goal length, maybe longer! YAY! And I thought I'd never use algebra. :happydance:

[birdiefu]

Hmm, I think in order to get a correct answer, I have to count the hairs on my head and/or save all my shed hairs in 24 hours. Ed's calculator gives me 32" and the linky Cinnamon Hair posted gave me 27". That was with guessing 100,000 hairs, 50 shed/day, and about 0.5" growth/month (which is about right, but I get more once in a while). I still have some layers left in my hair, but I think I might have another good 6-12" left till true terminal, which would be 42.5-48.5". I may not make it to knee, but hopefully at least classic will be in my future!

[Mely]

Didn't someone have it worked out based on taper? I think they assumed the taper was linear. Then you could imagine your pony tail to be part of an inverted cone. The top of your pony tail (where the elastic goes) would correspond to the base of the cone. Terminal length would be at the point of the cone. You could measure the diameter of your ponytail at the top, and at several other places along its length. From this you could work out terminal length, which would be where the diameter becomes zero (the point of the cone).

[nate]

Didn't someone have it worked out based on taper? I think they assumed the taper was linear. Then you could imagine your pony tail to be part of an inverted cone. The top of your pony tail (where the elastic goes) would correspond to the base of the cone. Terminal length would be at the point of the cone. You could measure the diameter of your ponytail at the top, and at several other places along its length. From this you could work out terminal length, which would be where the diameter becomes zero (the point of the cone).It's linear in the area, not in the diameter or circumference. Basically, find two points on your ponytail a fair distance apart and measure them. Let's say you take one at the nape of your neck and find a measurement of 3", and the other point is at BSL (12 inches lower, let's say) and has a circumference of 2.5". Then you can figure that for every 900 = 100 * 3^2 hairs you had at the nape, 625 survive to BSL. That means that one foot below you can expect 350, and one foot below that you can expect 75. So your terminal length would be a bit over 3 feet plus the measurement over the top of your head, which is something in the mid to upper 40s.

The formula: Take two circumference measurements, M1 and M2 at lengths H1 (higher up, smaller number) and H2 (lower down, larger number). Then:

Approximate Terminal Length = H1 + (M1^2 * (H2 - H1))/(M1^2 - M2^2)

In the above example, we get H1 = 10" (because the nape is around 10 inches in the LHC measurement system, which we want to use), H2 = 22", M1 = 3", M2 = 2.5", and the formula gives:

ATL = 10 + (9 * 12)/(9 - 6.25) = 10 + 39.3 = 49 inches.

(You can use centimeters instead if you want, since there are no constants in the formula.)

For any kind of reliability, you should take multiple measurements at different heights and average them. This method doesn't work well if you have layers (you must measure on a part of your length that isn't layered). Also, this can be messed up by any number of things, like periodic sheds. And, as people have pointed out, some hairs are just going to grow longer than others. So I wouldn't put much stock in this method, but it's nice in that it gives you a way to estimate without having to count the hairs on your head or your daily shedding.

[Saranne772]

I am SO confused I cant work out that formula at all!

But for the 1st link my hair apparently: Your growth potential is 59.46 inches. So as my current goal is 60 inches that is not too bad. I might just get there God Willing!

[DaveDecker]

Simple formula:

scissors = no

take good care of hair

wait many years

when length gains stop = terminal

:)

I know terminal length. My longest strands reached ankle, but there were only a few of them. And the length of the longest strands did not increase for 2 years.

[EdG]

It's linear in the area, not in the diameter or circumference. Great post nate!

A linear taper results from hair that grows to terminal length; falls out; and then starts over in the growth cycle. At any point in time, 50% of the hairs reach 50% of terminal length. While nicely explained by the growth cycle, the major problem with this theory is that all shedded hairs would be at terminal length, which simply doesn't match my experience.

An exponential taper results from hairs that fall out randomly, independent of length. The exponential taper is described by the length constant in the formula. 37% of all hairs will reach this length. This exponential taper can be derived mathematically (exponential decay is common in nature). This theory predicts that most shed hairs are short, which agrees with my experience. The main weakness of the exponential decay is that it does not place an upper bound on how long hair can grow!

I think real hair taper is a combination of both effects. It's probably not possible to accurately describe real hair taper in a simple formula. I'd do what DaveDecker suggests - just let it grow and find out for sure! :)
Ed

[Dianyla]

Didn't someone have it worked out based on taper? I think they assumed the taper was linear. Then you could imagine your pony tail to be part of an inverted cone. The top of your pony tail (where the elastic goes) would correspond to the base of the cone. Terminal length would be at the point of the cone.
Yep, I did this about 2 years ago. I put my hair into a banded ponytail and took measurements about every 6 inches, then figured out when circumference would approach zero. I'll have to go dig up the data from my old hair journal and see how it compares now that I've got a foot more of hair.

Also, I'm intrigued to try the linear regression based on the area, not circumference. Hmmm. :cool:

And, while I am interested in trying DaveDecker's formula... there's just one slight problem. Mine is starting to graze the floor, and it is still growing. I'd always planned on stopping at floorlength. :uhh:

[DaveDecker]

Also, I'm intrigued to try the linear regression based on the area, not circumference. Hmmm. :cool:

I would believe area, not circumference, is the factor.


And, while I am interested in trying DaveDecker's formula... there's just one slight problem. Mine is starting to graze the floor, and it is still growing. I'd always planned on stopping at floorlength. :uhh:

Later this year perhaps, reciprocal trims? :)

[EdG]

And, while I am interested in trying DaveDecker's formula... there's just one slight problem. Mine is starting to graze the floor, and it is still growing. I'd always planned on stopping at floorlength. :uhh:Dianyla, you are very fortunate! Everyone should have such a "problem"! :D
Ed

[Dianyla]

I would believe area, not circumference, is the factor.
Yeah, as soon as nate said that I realized "of course!" but it hadn't immediately occurred to me. Of course I suppose taking the log of all the circumference measurements would make it linear, as well, but anyways.


Later this year perhaps, reciprocal trims? :)
Hmmm... perchance there will be another grandiose DaveDeckerConIV hosted in the bay area? :D


Dianyla, you are very fortunate! Everyone should have such a "problem"! :D
Can't you just hear the sound of the world's smallest violin? :violin:

I predict that you will end up having such a similar "problem". :lol:

[EdG]

Can't you just hear the sound of the world's smallest violin? :violin:

I predict that you will end up having such a similar "problem". :lol:Hee, hee. :D

I look forward to having this "problem". I really can't tell whether I've reached terminal or not. My longest strands are still growing, but there are only a few tens of them left. :confused:
Ed

[Dianyla]

I look forward to having this "problem". I really can't tell whether I've reached terminal or not. My longest strands are still growing, but there are only a few tens of them left. :confused:
Ed
Mmm, hard to tell. :ponder: Could be just faster-growing leader hairs. Have you done a terminal length estimate on yourself, based on current thickness measurements?

[EdG]

Have you done a terminal length estimate on yourself, based on current thickness measurements?I actually haven't tried either method (measuring taper or shed strands). I probably should in the name of science!

My taper could be due to different rates of growth since I haven't had a trim since 2004. Or possibly due to breakage from (mostly) daily washing in a pre-LHC life :D Or maybe I am at terminal.

Despite my theories about terminal length, I don't have a clue about myself. :rolleyes:
Ed

[Dianyla]

I actually haven't tried either method (measuring taper or shed strands). I probably should in the name of science!
Uh, yeah! :uhh:

Though, I guess you're off the hook since you're an engineer, not a scientist. :p


My taper could be due to different rates of growth since I haven't had a trim since 2004. Or possibly due to breakage from (mostly) daily washing in a pre-LHC life :D Or maybe I am at terminal.
So many possibilities. Time will tell. :agree:

[DaveDecker]

Yeah, as soon as nate said that I realized "of course!" but it hadn't immediately occurred to me. Of course I suppose taking the log of all the circumference measurements would make it linear, as well, but anyways.

And this morning I reconsidered and realized (Duh!) that it is indeed logarithmic/exponential. Based on a linear rate of thinning from shoulder to mid-back, it would have maxed out just past waist. It seems to beg the question: is it truly a logarithmic progression, or would it have been linear in the absence of some unknown cause of damage? (maybe friction on the braid from the seatback of chairs?) Hmm...



Hmmm... perchance there will be another grandiose DaveDeckerConIV hosted in the bay area? :D

That is indeed the plan, man! Is it too early to announce on the Meets forum? :silly:

[Dianyla]

That is indeed the plan, woman! Is it too early to announce on the Meets forum? :silly:
Um... it may be a wee bit early! :p

[EdG]

And this morning I reconsidered and realized (Duh!) that it is indeed logarithmic/exponential. Based on a linear rate of thinning from shoulder to mid-back, it would have maxed out just past waist. It seems to beg the question: is it truly a logarithmic progression, or would it have been linear in the absence of some unknown cause of damage? (maybe friction on the braid from the seatback of chairs?) Hmm...I think so.

An exponential taper implies that the main limiter is random breakage. This is good news for super longhairs because it implies that hair taper is limited by something one can control (breakage) as opposed to something one can't do anything about (growth cycle). :)

I think both effects - random breakage (exponential decay) and growth cycle (linear decay) - are present, just in differing ratios depending on the person. Super longhairs have a long enough growth cycle so that random breakage dominates. Longhairs who are terminal at waist-length are limited by the growth cycle.

This is my theory, with the disclaimer that I am not a scientist. :D
Ed

[Dianyla]

I think both effects - random breakage (exponential decay) and growth cycle (linear decay) - are present, just in differing ratios depending on the person. Super longhairs have a long enough growth cycle so that random breakage dominates. Longhairs who are terminal at waist-length are limited by the growth cycle.
I think you're really on to something with the breakage vs. growth limitations. I'm sure most of my issue is breakage, as I seem to have a fairly long growth cycle. Going just by average growth rate I must have at least a 10 year follicle lifespan, so far.


This is my theory, with the disclaimer that I am not a scientist. :D
Theory? Or hypothesis? :misskim:

[EdG]

I think you're really on to something with the breakage vs. growth limitations. I'm sure most of my issue is breakage, as I seem to have a fairly long growth cycle. Going just by average growth rate I must have at least a 10 year follicle lifespan, so far.


Theory? Or hypothesis? :misskim:Thanks. So far it's a hypothesis. I'd love a proof! :D

I've modeled both effects (individually). Maybe I need to put together a combined model. :)
Ed

[DaveDecker]

Um... it may be a wee bit early! :p

No doubt! Asking the question was just me being silly. :D



I've modeled both effects (individually). Maybe I need to put together a combined model.

We ultra-longhairs could start with a heuristic sampling method by taking circumference measurements at specific intervals down the length, then try to match either a curve or a straight line to the area of the (hypothetical!) ponytail cross-sections -- individually and grouped -- and try to find the best fit to determine the most appropriate distribution.... er, nevermind. :)

[Dianyla]

No doubt! Asking the question was just me being silly. :D
And besides, does something that's going on to be the fourth annual event really even need announcing? :p


We ultra-longhairs could start with a heuristic sampling method by taking circumference measurements at specific intervals down the length, then try to match either a curve or a straight line to the area of the (hypothetical!) ponytail cross-sections -- individually and grouped -- and try to find the best fit to determine the most appropriate distribution.... er, nevermind. :)
I sense a research project coming on... :)

[lilalong]

this tread just cracks me up.

[constantki]

Using this formula, apparently my estimated terminal length is 19 inches? My hair is already past 30. . .
Are there really a statistically significant number of people with a terminal length less than 20" or is my math just wrong?

[Igor]

Using this formula, apparently my estimated terminal length is 19 inches? My hair is already past 30. . .
Are there really a statistically significant number of people with a terminal length less than 20" or is my math just wrong?

Yes, you have done something wrong. There is no way that is correct for a iii-head

[nightwish90]

double post, sorry

[nightwish90]

i know this is old, but this may help ANYONE to understand:




<number of lost hairs every day>*365= <number of lost hair per year>
.....
so now, you need to know how many years are necessary in order to lose every of your hairs once

<number of all hairs > / <number of lost hair per year>=<how many years you need to lose all of your hairs once>

=>that means this is the cycle of your hair, none of your hairs lives longer


so now multiply with how many inches your hair (naturally) gains per year


i really hope this helped everyone understand
____________________________________


now i'm particularly interested in how i could make my hairs live longer??? for me it seems i lose at least 100 hairs/day ...so my hair might live less than 3 years, but i doubt i have 100.000 hairs on my head though. any help? i want thicker, long living hair, i don't know what to do to help this :confused:

[Long_hair_bear]

owwwwwwwww my head hurts LOL

I'm going to take the easy way out and just wing it.When my hair stops growing after all I've done to speed it along(short of a major cut)that's when I know I've reached terminal.

Or at least a slowing down point.

Ya I'm with you. I hate math and don't want to count all my "individual hairs". :D

[battles]

I just tried it out and ended up with a 54 inch terminal. That's eh... mid-calf or so on me.

[Diamond.Eyes]

I calculated my terminal length, and it is insane :bigeyes:! It's great to know that I could one day have hair that drags on the floor! :joy:

[candycandace]

I calculated my terminal length, and it is insane :bigeyes:! It's great to know that I could one day have hair that drags on the floor! :joy:
Aww man! My term length was only 50.2 inches...which is knee length for me. No floor dragging here lol. What was yours?

[Diamond.Eyes]

Aww man! My term length was only 50.2 inches...which is knee length for me. No floor dragging here lol. What was yours?
127.55 inches XD. I will probably never have it that long though lol.

[ArienEllariel]

hmm. mine was 37.9in. but then again, my hair doesn't necessarily grow that quickly and some months it doesn't seem to grow at all. This would be a little past tailbone for me. I really hope it will grow longer than that... :/ I'm not in the best of health either so this may not really be my real terminal. I refuse to believe that I can't make it to classic. *hurmph*

Hang on a second... I lose somewhere close to 20 hairs a day. Sometimes more. I put in 30 and got this result but if I put in 20, I get something like 61.5in. (which would be floor length and a little beyond) Huge huge difference. ?

[Mommyof4]

With this formula, my terminal length would be: 164 inches?? I'm not seeing that happen.. I would LOVE for it to, but it seems to good to be true! If I can get 60 inches, I'll be happy!

[Diamond.Eyes]

hmm. mine was 37.9in. but then again, my hair doesn't necessarily grow that quickly and some months it doesn't seem to grow at all. This would be a little past tailbone for me. I really hope it will grow longer than that... :/ I'm not in the best of health either so this may not really be my real terminal. I refuse to believe that I can't make it to classic. *hurmph*

Hang on a second... I lose somewhere close to 20 hairs a day. Sometimes more. I put in 30 and got this result but if I put in 20, I get something like 61.5in. Huge huge difference. ?
I also noticed that. I lose between 10-15 hairs a day and if I put 15 it was at ninety-something and if I put 10 it was like 152 inches. I just put 13...it really is a big difference.

[ArienEllariel]

I also noticed that. I lose between 10-15 hairs a day and if I put 15 it was at ninety-something and if I put 10 it was like 152 inches. I just put 13...it really is a big difference.

Hmm. So I'm guessing the terminal answer thing really is "I don't know" more than what you can actually expect.

[Diamond.Eyes]

Hmm. So I'm guessing the terminal answer thing really is "I don't know" more than what you can actually expect.
I think you are correct. :laugh: Hair is so unpredictable.

[battles]

hmm. mine was 37.9in. but then again, my hair doesn't necessarily grow that quickly and some months it doesn't seem to grow at all. This would be a little past tailbone for me. I really hope it will grow longer than that... :/ I'm not in the best of health either so this may not really be my real terminal. I refuse to believe that I can't make it to classic. *hurmph*

Hang on a second... I lose somewhere close to 20 hairs a day. Sometimes more. I put in 30 and got this result but if I put in 20, I get something like 61.5in. (which would be floor length and a little beyond) Huge huge difference. ?

Ohhh. I didn't know it made that huge of a difference, I had increased mine too to be on the safe side. I barely shed at all, and if I go for what I think is more accurate I end up with well over 100 inches.

[aisha.christine]

I keep getting huge numbers! UGH
I feel like I'm not doing this right. :(

Check my math?

Because my hair is basically brunette, I went off of igor's guesstamation as to how many hairs I should have on my head: 100,000

I shed between 15 and 20 hairs a day.

I used my total yearly growth, 9 inches.

So, I calculated my yearly shed rate with 15 hairs a day- 5475
I then divided 100,000 by 5475
I got 18.26
I then multiplied 18.26 by 9 inches.

I got 164.

I then used 20 shed hairs.

Yearly shed rate- 20*365=7300

How many years it would take to lose all of my hair- 100,000/7300= 13.7

Estimated terminal length- 13.7*9= 123


I then used 17.5 hairs because it's the average of 20 and 15.

Yearly shed rate- 17.5*365= 6387.5

How many years it would take to lose all of my hair- 100,000/6387.5=15.66

Estimated terminal length- 15.66*9= 140


I then calculated the average of all three numbers- (140+123+164)/3= 142 in.


Should I go with the average?

[Sushi144]

The first formula gives me 27 inches. I'm already at 34. :lol:

[long&blonde]

Um, How do I figure the number of hairs on my head? And, the mess I clean outa my shower drain, I'm supposed to be drying,separating,counting?
Hmmmmmmmmmmmmmmm..And here I thought my lackadaisical nature stopped at how often I don't change my sheets. Separate colors when I wash. A few more etc.'s.
Cool formula tho:just to see;for any who could figure it out!

[nightwish90]

I also noticed that. I lose between 10-15 hairs a day and if I put 15 it was at ninety-something and if I put 10 it was like 152 inches. I just put 13...it really is a big difference.


10-15 hairs??? what do you do???what do you eat?? you have so much hair on your head and you shed only 10-15??? how is this possible...

[terylenerose]

I followed this link: http://www.allvidzhaze.com/phptest/hairgrowth.html
I put in 110000 hairs on my head, 0.6 inches per month and 100 hairs lost per day. And you know what I got? 13.33 inches. :rolleyes::confused: I'm already at 23, or my tape measure has some serious issues. Who has that short of a terminal length?

[door72067]

the web link calculator thingy gave me 65.________ (I didn't absorb the rest of the number) of potential


I am 65" tall LOL

[spidermom]

I got a lower number than the length I already have, too. I think the formula is worthless.

[Silverbrumby]

My calculations:

100,000

Shed hair per day, average 80 =

29,500 per year

100,000 / 29,500 =

3.8 years till all hair is shed.

Growth rate 1/2 inch a month for 6 inches per year. Lets be generous and say 7 ;-)

3.8 x 7 = Max growth 26.6

This 26.6 is NOT the LHC length calculation which is from the front of the hair line going all the way over to the back.

I'd be over the moon with 26.6 for an individual hair strand. Currently my longest I've measure that has fallen out is 18 inches so this is a full 8.6 inches longer than that! That would put me at waist length.

Now being conservative I'll use 5 inches a year taking in an inch trim per year.

3.8 x 5 = 19 inches

See. That's what I'm finding right now with trimming. Nineteen inches seems to be around my terminal with a few hardy hairs growing past that. When I grow to 18 inches or 26 by the LHC measurements I get sever tapering.

So the solution might be no trims to get to the max. growth and then trim from there. Just thinking out loud.

[julierockhead]

Before doing any calculations, watch this, very helpful stuff!

http://www.youtube.com/watch?v=DfCJgC2zezw

[terylenerose]

snip
This 26.6 is NOT the LHC length calculation which is from the front of the hair line going all the way over to the back.
snip
I thought of that too, but it still doesn't make any sense. 13.33 inches? Seriously? I've had longer lengths than that measured any way you want. Terminal strand length should be about 36"-48".

[natt i nord]

The link terylenerose mentioned gives me 10.10 inches, the formular mentioned in the first post gives me at least 16,4 inches.

Uhm well, I'm already at around 25". I think both formulas don't make any sense...

[jadelouise]

I'm assuming an exponential decay

n=exp (-length/length_constant)

where length_constant is given by (12*I*G)/(365*S) as Naluin said.

exp (-1) is 37%.

I have some graphs on my website illustrating this http://www.edgrochowski.com/haircare.htm

Hope this helps. :)
Ed

WOAAAHHH someone's clever! long hair and intelligence ;D