# formula for computing seat tube angle

#### robbielg

##### New Member
the formula i found in the bicycle sizing article here for computing top tube and seat tube lengths is great. However i cant seem to work the formula for the seat tube angle. Any engineers or math wizs here ?

"For the seat tube angle you first of all need to measure your thigh and lower leg lengths. Thigh length is measured horizontally from the upright support to the front of your kneecap, whilst the lower leg length is measured from the top of your kneecap vertically to the ground. Then calculate the seat tube angle as: Cosine of 26.4% (thigh length / lower leg length). The answer should be taken to the nearest 0.5 degree. "

heres my computation cos(.264)(59/52.5) = 0.9999

Admittedly, I'm a bit of a newb, but does it really matter that much? The effective seat tube angle can be changed by a few degrees with fore-aft of the seat anyway. If you were getting a custom frame, this may be more important, but will you have much say over a standard store-bought anyway? I'm not being argumenative--I really don't know, but I suspect it's not a big deal to worry about, plus the angle changes from road to time trial geometry generally, anyway!

Skoorb said:
Admittedly, I'm a bit of a newb, but does it really matter that much? The effective seat tube angle can be changed by a few degrees with fore-aft of the seat anyway. If you were getting a custom frame, this may be more important, but will you have much say over a standard store-bought anyway? I'm not being argumenative--I really don't know, but I suspect it's not a big deal to worry about, plus the angle changes from road to time trial geometry generally, anyway!
It isnt a big deal if you are comfortable on standard store bought roadbikes.
But ive never been really comfortable on my roadbikes like i am on my mountainbikes.

using the bike sizing formula in the article in this forum my top tube lenght should be 52 while my seat tube angle should be 72.7 degrees. This could be key why i could never get comfy on a roadbike

bikes with a slack seat tube angle of 72 come with a long top tube lenght of way longer than 52. And bikes with a short top tube of 52 come with a steep seat tube angle of about 75 degrees.

robbielg said:
It isnt a big deal if you are comfortable on standard store bought roadbikes.
But ive never been really comfortable on my roadbikes like i am on my mountainbikes.

using the bike sizing formula in the article in this forum my top tube lenght should be 52 while my seat tube angle should be 72.7 degrees. This could be key why i could never get comfy on a roadbike

bikes with a slack seat tube angle of 72 come with a long top tube lenght of way longer than 52. And bikes with a short top tube of 52 come with a steep seat tube angle of about 75 degrees.
FWIW. I agree with Skoorb that the adjustment you want can PROBABLY be accommodated with the seatpost if you select a frame which uses a 27.2 seatpost ... perhaps, also, if the seatpost size is 31.6 ...

Particularly since 73º is a VERY COMMON seat tube angle ... or, at least, it was at one time.

And, seatposts with between ZERO setback to those with over-an-inch of setback are readily available (EASTON also makes less expensive aluminum seatposts that have the "extreme-by-comparison" setback that their carbon fiber seatposts have) to accommodate the 0.3º difference which can't be more than three millimeters on frame with a 52cm top tube. Is it more?

Just where do you want to situate your saddle that you can't with any of the seatposts & saddles that are available -- further forward OR further back?

Now, I'm not even going to begin to suggest how a MTB rider should set up his/her bike ... and, I guess I should only hint at how a ROAD rider should set up his/her ...

BUT, to begin, I'll bet the odds are pretty high that YOUR mountain bike has 175mm cranks, and your various road bikes have NOT had THAT length crank arms in the past.

Now, if I actually rode my covered-with-dust MTB with any frequency, I suspect I would be a strong candidate for a "flat bar" ROAD bike ... I've certainly got the "extra" parts ... but, I know that the bike would probably not see too many miles -- not everyone can move seamlessly between MTB & ROAD.

The handlebar on your MTB(s) is probably HIGHER than on your ROAD bike(s) in relation to the top of the respective saddles ... the current trend (in the past couple of decades!) has been smaller ROAD frames which places the handlebars lower than in the distant past. You could possibly choose a larger frame OR a "comfort" HYBRID frame whose headtube is taller and situates the handlebars in a more higher/MTB-like relation to the saddle (some people do have their MTB stems in a competitively lower placement -- do you?).

Your MTB has FATTER tires and/or a suspension system which adds to some of the perceived comfort ...

All of that is to say/suggest that a reason you aren't comfortable on your ROAD bike(s) may simply be because you probably aren't comfortable in the riding position ... but, a "flat bar" ROAD bike may be what will resolve your discomfort -- i.e., you are tweaking when you should probably be rethinking!

The result of (.264)(59/52.5) is the cos of the angle.
In order to get the angle itself you would need inverse cos (acos).
(.264)(59/52.5) = 0.2966
acos(0.2966) = 72.74º

ttopaz said:
The result of (.264)(59/52.5) is the cos of the angle.
In order to get the angle itself you would need inverse cos (acos).
(.264)(59/52.5) = 0.2966
acos(0.2966) = 72.74º
thanks ttopaz, forgot my high school trigonometry completely, didnt do the INVERSE cos part. had my mech engineer brother compute it and he got 72.74 too

alfeng, you guessed right about a lot of things, yes my mtb has higher bars, it has 175mm cranks which i have changed to 170 to ease discomfort in my knees. My other roadbike has been converted into a flat bar hybrid. I am more comfortable on the mtb because of the riding position. I have had problems with some roadbike frames ive had not being able to get the saddle far back enough.

the reason im making a big deal of this is because i am interested in a specialized roubaix elite triple roadbike. The specialized dealer here is a friend. The main selling points of the roubaix is its comfortable riding position and smooth ride.

but the roubaix with a 52cm top tube has a seat tube angle of 75.5 ! a big difference from my ideal 72.74

the dealer here doesnt have the actual bike in stock and will have to order it for me from the usa. they told me to be sure about the size because once they order it i must buy it. and with tax and shipping it costs more than 2000 dollars. that would be my most expensive bike. If only they had the actual bike here it would be easier.

I have knee, back, and flexibility issues too and am well into middle age and have been off the bike for 3 years. I have proportionally shorter arm and torso lenght and long leg and foot lenght.

ive been in a 540km 3 stage roadrace 11 years ago that i didnt finish.
and am dreaming of riding one of its stages again, a 230km ride through the mountains to a nice vacation place on the other side of the island

alfeng said:
Particularly since 73º is a VERY COMMON seat tube angle ... or, at least, it was at one time.
I think the OP's situation is that he rides a very small frame size...my wife needs a 44cm frame and her seat tube is 75 degrees...for frames less than 52 cm it is very rare to find a seat tube at less than 74 degrees. To the OP, you may just need to find a seatpost with enough setback to allow for the same positioning as a 72.7 seatpost. As for your flexibility, you might want to get a 15 degree stem rather than the more common 6-8. Hope you're able to solve your fit issues and welcome back to cycling.

ive been in a 540km 3 stage roadrace 11 years ago that i didnt finish.
and am dreaming of riding one of its stages again, a 230km ride through the mountains to a nice vacation place on the other side of the island
Nice goal

BTW, I'm not even close to middle age and have knee and flexibility problems, so you're not alone!

You can grossly shallow out the seat tube angle with a seat with major set back. Profile makes a seat designed for people who want a more aggressive seat angle, but surely there is one with far more rear offset available, including a seat with really long rails.

I suppose you've also addressed your knee pain through technique (like knees being up and down only and close to the top tubes, for instance, something it took me a long time to learn) and strengthening/stretching--just throwing it out there!

GL.

robbielg said:
thanks ttopaz, forgot my high school trigonometry completely, didnt do the INVERSE cos part. had my mech engineer brother compute it and he got 72.74 too

alfeng, you guessed right about a lot of things, yes my mtb has higher bars, it has 175mm cranks which i have changed to 170 to ease discomfort in my knees. My other roadbike has been converted into a flat bar hybrid. I am more comfortable on the mtb because of the riding position. I have had problems with some roadbike frames ive had not being able to get the saddle far back enough.

the reason im making a big deal of this is because i am interested in a specialized roubaix elite triple roadbike. The specialized dealer here is a friend. The main selling points of the roubaix is its comfortable riding position and smooth ride.

but the roubaix with a 52cm top tube has a seat tube angle of 75.5 ! a big difference from my ideal 72.74

the dealer here doesnt have the actual bike in stock and will have to order it for me from the usa. they told me to be sure about the size because once they order it i must buy it. and with tax and shipping it costs more than 2000 dollars. that would be my most expensive bike. If only they had the actual bike here it would be easier.

I have knee, back, and flexibility issues too and am well into middle age and have been off the bike for 3 years. I have proportionally shorter arm and torso lenght and long leg and foot lenght.

ive been in a 540km 3 stage roadrace 11 years ago that i didnt finish.
and am dreaming of riding one of its stages again, a 230km ride through the mountains to a nice vacation place on the other side of the island
Okay, the difference between 72.74 & 75.5 is significant IF one of the current Easton seatposts won't set your saddle back far enough for you ...

BTW. I'm not sure what your idea of a proportionally shorter arm & torso are. To be properly fitted for a frame with a 52cm top tube, you need to be in the 5'5" +/- height range. Is that right?

When you are seated on a hard kitchen-type chair AND sitting straight, what is the measurement to your shoulder bone? What is the measurement of that bone to the crook between your thumb and the rest of your hand?

Regardless, the Specialized Roubaix Elite is not going to be a good deal for you if the frame's geometry doesn't work for you ...

BUT, in that regard, you should read Keith Bontrager's article "The Myth of K.O.P.S." and/or Sheldon Brown's article on frame sizing:

FWIW. Regardless of the frame size (seat tube & top tube) of my various ROAD bikes (and, it varies greatly), the variation is probably less than a half-inch from the bike with the most forward reach to the least. I establish my saddle's position according to the crank (I prefer 175mm, but have 172.5 & 170mm on some ... and, have some 180mm cranks that I just haven't gotten around to fiddling with [generally, more leverage == less "strain" ... apparently, based on hearsay, the benefits of leverage are diminished with/by KOPS] ... I don't use KOPS), and then I choose the stem length accordingly (some handlebars have a variation in the reach which is why there is a slight deviation from my preferred setup on some of my bikes).​

That's a wordy way of suggesting/saying that you want to replicate the position of the bike(s) which you find to be most/more comfortable to ride AND eschew fashion.

A "touring" frame will probably give you the slacker angles you want ... the FUJI & TREK touring bikes are in the \$1000-to-\$1200US range. For the difference to whatever the Specialized Elite costs (MSRP of 2x by my reckoning), you can swap the components you aren't keen on with whatever you would like OR use the drivetrain that I would recommend for your intended ride -- a Campagnolo "group" ... Veloce or Centaur (better), or a "mix" of Veloce & Centaur components ... a "compact" crank (I don't think there is an Ultra Torque triple) and a 12/13-29 cassette. Campagnolo ERGO shifters downshift flawlessly under load (i.e., you're already on an incline and want to access a larger cog in the rear!), IMO ... I was going to say that the Campy shifters downshift BETTER, but then all the proponents of Shimano (whom I love for what they have done for cycling AND who have superior customer service & great components) & SRAM (who have inferior customer service, IMO; but, interesting components) would feel that they need to chime in to defend their component selection.

A HYBRID frame will almost certainly give you the frame angles you want, too.

alfeng said:
Okay, the difference between 72.74 & 75.5 is significant IF one of the current Easton seatposts won't set your saddle back far enough for you ...

BTW. I'm not sure what your idea of a proportionally shorter arm & torso are. To be properly fitted for a frame with a 52cm top tube, you need to be in the 5'5" +/- height range. Is that right?

When you are seated on a hard kitchen-type chair AND sitting straight, what is the measurement to your shoulder bone? What is the measurement of that bone to the crook between your thumb and the rest of your hand?

Regardless, the Specialized Roubaix Elite is not going to be a good deal for you if the frame's geometry doesn't work for you ...

BUT, in that regard, you should read Keith Bontrager's article "The Myth of K.O.P.S." and/or Sheldon Brown's article on frame sizing:

FWIW. Regardless of the frame size (seat tube & top tube) of my various ROAD bikes (and, it varies greatly), the variation is probably less than a half-inch from the bike with the most forward reach to the least. I establish my saddle's position according to the crank (I prefer 175mm, but have 172.5 & 170mm on some ... and, have some 180mm cranks that I just haven't gotten around to fiddling with [generally, more leverage == less "strain" ... apparently, based on hearsay, the benefits of leverage are diminished with/by KOPS] ... I don't use KOPS), and then I choose the stem length accordingly (some handlebars have a variation in the reach which is why there is a slight deviation from my preferred setup on some of my bikes).​

That's a wordy way of suggesting/saying that you want to replicate the position of the bike(s) which you find to be most/more comfortable to ride AND eschew fashion.

A "touring" frame will probably give you the slacker angles you want ... the FUJI & TREK touring bikes are in the \$1000-to-\$1200US range. For the difference to whatever the Specialized Elite costs (MSRP of 2x by my reckoning), you can swap the components you aren't keen on with whatever you would like OR use the drivetrain that I would recommend for your intended ride -- a Campagnolo "group" ... Veloce or Centaur (better), or a "mix" of Veloce & Centaur components ... a "compact" crank (I don't think there is an Ultra Torque triple) and a 12/13-29 cassette. Campagnolo ERGO shifters downshift flawlessly under load (i.e., you're already on an incline and want to access a larger cog in the rear!), IMO ... I was going to say that the Campy shifters downshift BETTER, but then all the proponents of Shimano (whom I love for what they have done for cycling AND who have superior customer service & great components) & SRAM (who have inferior customer service, IMO; but, interesting components) would feel that they need to chime in to defend their component selection.

A HYBRID frame will almost certainly give you the frame angles you want, too.
Im 5'8" and my shoe size is 45. Ive told my lbs not to order the roubaix. I will only consider that bike again if i can get to actually sit on one.

Thank you for the sheldonbrown link, its very relevant and interesting.

i prefer the roubaix over a touring or hybrid frame because i also want performance and speed with comfort

robbielg said:
Im 5'8" and my shoe size is 45. Ive told my lbs not to order the roubaix. I will only consider that bike again if i can get to actually sit on one.

Thank you for the sheldonbrown link, its very relevant and interesting.

i prefer the roubaix over a touring or hybrid frame because i also want performance and speed with comfort
FWIW. It's great having a nice frame/bike OR one that you like to look at when the bike is static. Having said that, I suspect that I am in a minority camp (maybe, the only person in this Forum who will openly say so!) that thinks that, for the most part, the frame (presuming it is sound) is merely something to hang the components on.

The geometry does matter, to some extent ... but, not so much for common folk, IMO.

There are reasons for a shorter (~1 meter) wheelbase, but for MOST riders, it is more of a cosmetic issue ... you cannot cut an equally tight arc with a longer wheelbase bike, but if you aren't Crit racing, I don't see the real need.

If you think that non-Crit handling, in general, is diminished by a longer wheelbase, well ...

All you have to do is observe the ease that a good tandem captain can take his/her REALLY LONG wheelbase bike through a turn.

Nicer wheels + the crankset/BB and/or shifters will ensure better performance than the "stock" setup that usually comes on all but the high-zoot bikes.

BTW. At your height of 5'8", without knowing the particulars, I suspect you can readily/comfortably use/fit/ride a 52cm (c-c) frame with a 54cm top tube and a 9cm stem ...

hmm.. from experience i think a 54 top tube will be a bit stretched out for me.

womens specific frames are designed with womens shorter upper body/longer legs in mind. I wonder if a such a frame could work for me. they come in girly colors tho

robbielg said:
hmm.. from experience i think a 54 top tube will be a bit stretched out for me.

womens specific frames are designed with womens shorter upper body/longer legs in mind. I wonder if a such a frame could work for me. they come in girly colors tho
HMmmm ...

Okay, I'm 5'9" ...

Mostly, I've been riding my old 52cm Peugeot frame (54cm top tube + 120mm stem). My bars are about 2" below the top of the saddle and the top of the hoods is a little lower than that.

As I said, all of my various bikes all have the same (within a half-inch on the reach ...) fit regardless of the frame size where the stem's length "corrects" for the varying top tube lengths.

Realizing that everyone's physiology is different, I still reckon that at 5'8", a 54cm top tube + a 80mm-or-90mm stem (more than an inch shorter than MY stem) which may-or-may-not be rigged HIGHER (a higher stem has the same net effect as a shorter top tube) should be comfortable/doable for you ... OR, you should give serious consideration to taking Yoga classes for a few weeks/months to improve your general flexibility.

BTW. Perhaps, most of the women I know do NOT ride WSD bikes because they don't like the paint scheme on those bikes, too!?!

Skoorb said:
Nice goal

BTW, I'm not even close to middle age and have knee and flexibility problems, so you're not alone!

You can grossly shallow out the seat tube angle with a seat with major set back. Profile makes a seat designed for people who want a more aggressive seat angle, but surely there is one with far more rear offset available, including a seat with really long rails.

I suppose you've also addressed your knee pain through technique (like knees being up and down only and close to the top tubes, for instance, something it took me a long time to learn) and strengthening/stretching--just throwing it out there!

GL.
thanks for the encouragement. yes ive been watching my pedaling technique, been stretching too, and strengthening my whole body at the gym. Stretching really helps.

alfeng, you are right a 54 top tube will fit me (IF it has a 72 degree seat angle.) If not, (which is almost always), i would have to move my saddle back 2 cm which makes the efective top tube a too stretched out 56 for me.

its either i get a small frame and raise the handlebars ( some manufacturers cut the steerer so this could be a problem), or get a larger frame and get a shorter stem (easier to do in my opinion)

there's a size 51 jamis ventura comp at my local bike shop that i now have my eyes on, its half the price of the roubaix. it has a 52.5 top tube. Its a bit comfort oriented too with its longer chainstays, higher bars and shorter top tube, and it has carbon forks and seatstays! But with its 74 dgree seat tube(normal for this size) i have to move my saddle way back and with the stem flipped and at the higest position and the saddle at my preferred rearward position the bars(the hoods) still seem a tad far and low for me. It has a 90mm 6 degree stem.

If i get the jamis i plan to change the seatpost to one with more layback, , shorter stem with more rise , and handlebars with shorter reach to the hoods and drops. Its a pity all these factory parts are nice and light easton ones.

Got this Jamis ventura comp 2 days ago. Im still tweaking the saddle, bar and lever position for comfort. Bike feels small which i like. It has carbon forks and seatstays but the ride is not as plush as i expected. My cheap old aluminum beater bike is wayy more plush, dont hnow why. I also copied the old bikes position but the new one still isnt as comfy as the old bike. was planning to sell the old bike, now im not selling.

according to jamis website the seat angle is 74 and effective top tube is 52.5 for my size 51 bike. I have my saddle all the way back on the seatclamps, and the seat post is the laid back type.

With the bars at the highest position the bars are just 2 cm lower than my saddle so it should be comfortable, but i want more comfort. Saddle is wtb shadow V. My comfortable old bike has a crossbow saddle which costs 1/6 the price of the wtb and seems more comfy.

I know my weak core and flexibility isnt entirely to blame because im comfy on my old bike.

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