Handlebar stem : height vs length

I want to decrease the reach of my handlebars. Does it matter whether I increase the height or get a stem with a smaller length(extension?) on my bike?

And is there any way to calculate the relation between the two? Something like, a 1 cm increase in height is equivalent to a 1.5 cm increase in length?

Background : I have an old single bolt handlebar stem(see image) with it's minimum insertion not visible(if it ever had one). When I raised it enough for it to be somewhat comfortable it started creaking every time I put power while pedaling or while climbing off the saddle. I have another similar stem that is slightly more than 1 cm longer but has it's minimum insertion about 3 cm higher than what the current one does not creak at. I want to know whether it will really reduce the distance I have to extend forward. Yes seems to be the intuitive answer but I really want to know for sure because these are a big bother taking off and putting on.

Edit : The handlebars I mention are drops on a road bike.
The horizontal portion is parallel to the ground

• Isn't the horizontal portion parallel to the ground by definition? Commented Mar 6, 2014 at 16:57
• @A.E.Drew - You've obviously never seen a bike with the "drop" bars twisted 180 with the bottom of the U up. Commented Mar 6, 2014 at 20:10
• I don't know that there's any formula. Depends a lot on what is the specific cause of a misfit. If it's purely a too-big bike or a short torso then you simply want to cut the reach. If it's (at least in part) a lack of torso flexibility (or simply an uncomfortable feeling in an oversized gut when you lean forward too much) then you probably want both. (In my (limited) experience replacement stems tend to combine both features -- simultaneously taller with less reach. Though of course this is all out the window with threadless.) Commented Mar 6, 2014 at 20:13
• Note that you can just push the stem further into the bike to avoid the height gain, if you like. It's unlikely that it will be long enough to bottom out (but if it is, make sure it's not bottomed out as you need to push it down to free it)
– Móż
Commented Mar 6, 2014 at 23:40
• @DanielRHicks and A.E. Drew : I meant that the horizontal portion of the handlebar stem is parallel to the ground. I should have been more clear Commented Mar 7, 2014 at 12:12

The answer is trigonometry. Most bikes have a headset angle of about 74°, give or take a degree. Over the adjustment range you're looking at that degree doesn't make a difference.

Here, tan(74 degrees) = height change / reach change = ~3.5. So to get a centimetre of reach change to need to lift the stem 3.5cm, putting the stem up reducing the reach. Or you can invert that and say each centimetre you lift the stem changes the reach by about 3mm.

Roughly, the stem that's about 1cm longer but 3cm higher will have the same reach. But 3cm higher will feel quite different, and because of the way your body curves to reach the bars it will probably feel as though the reach is shorter.

• The distance from the center of my seat to the center of the handlebars appears to change only by around 3-4mm due to a 3cm increase in height of the handlebars(without any vertical change in length). Surprising how much difference in comfort such a small change makes. Commented Mar 7, 2014 at 13:11

I always use a spreadsheet to make stem, spacers and handlebar calculations. I find it makes best sense when comparing one setup, that exists and I have used, with another that might be real or hypothetical.

Here's an example where I'm considering changing the Pro Vibe 7s on my track bike to a Deda Newton deep drop and if I need to change the stem and/or spacers.