Calculate frame stack and reach

Is is possible to calculate stack and reach for framesize 63?

• possible duplicate of Handlebar stem : height vs length Commented Mar 18, 2014 at 19:27
• Hmmm. They stop just short of giving you enough info to calculate everything. Commented Mar 18, 2014 at 22:38
• @DanielRHicks - Probably because it's a road frame, not a TT frame and stack/reach is somewhat irrelevant. Commented Mar 19, 2014 at 15:06
• @JohnP - But my point is that from those dimensions you can't calculate any of the other dimensions. Can't even calculate the height of the top bar relative to the axles. Can't calculate the height of the BB relative to the axles. Commented Mar 19, 2014 at 15:40
• @JohnP: Stack and reach are pretty much the only relevant frame dimensions. What do I care about down tube, head tube, fork or seat tube length? Commented Feb 24, 2018 at 17:53

Yes! Well, sorta. You can get an approximation using.... ~~trigonometry~~

In order to get an accurate reading, you'll need to divide the frame up into right triangles. We'll assume that the top tube is horizontal, parallel to the ground. This makes everything much easier because you automatically get right angles. However, many bikes will have sloping top tubes, which complicates the work. The first step therefore is to determine what slope the top tube has. For this particular example, the chart gives measurements that strongly suggest the top tube is horizontal, or even downward sloping, so this method is likely viable, but double check anyways.

But anyways, assuming a horizontal top-tube parallel to the ground, here's your frame broken up into right angles and the proof for stack height:

We want to find the stack height, which is length l.

• l = p = n
• top tube and ground are parallel; therefore, the line segments perpendicular to them are congruent lengths, and because everything is either parallel or perpendicular, all their vertices are right angles.
• ∠EHC = EGC = 90°
• As per the rule above.
• ∠ECG = 73°
• This is the seat-tube angle, given by the geometry chart.
• ∠HCE = 17°
• 90° - 73° = 17°
• k = 63cm
• cos(17°) = p / 63cm
• cos is the adjacent over hypoteneus (♪ soh-CAH-toa ♪)
• p = cos(17°) × 63cm
• p = 60.25cm
• now, because p = l, the stack height l must be 60.25cm. ∎ Here's the diagram again with all the measurements filled out:

Now calculating the reach is easy. We know the height of the stack is 60.25cm, which is one side of a right triangle with a hypotenuse of 63cm. Knowing this you can use the Pythagorean theorem to determine the remaining side, a segment of the top tube is 18.41cm. We also know the full length of the top tube is 59cm, so the remaining segment must be 59cm - 18.41cm = 40.59cm. And that's your reach!

Hope this helps, and hope my math isn't too bad here!

• The math is correct, but it looks like 63cm is measured to the top of seat clamp which is a rather useless measurement. Stack is supposed to be measured to to handlebars, so headset dimensions matters too.
– ojs
Commented Feb 26, 2018 at 18:22
• yeah, good catch. i haven't seen any seat tubes that extend more than an inch or so past the top tube so it shouldn't muck up the measurements too much hopefully. Commented Feb 28, 2018 at 5:15

This calculator here http://bikegeo.muha.cc/ may be helpful. It looks as though it's meant to calculate geometry changes resulting from a fork swap, but it does give you stack and reach.