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#### dontimberline

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Ok - can anyone figure this out for me:

If I want to swap out a +17 degree stem for a +6 degree stem, both being 90mm C-C, how much vertical drop in the handlebar height can I expect?

I think it's basic trigonometry using the law of cosines, but it's been a long time and I can't for the life of me remember how to figure it out!

#### Mark McM

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Stem rise and angle

dontimberline said:
Ok - can anyone figure this out for me:

If I want to swap out a +17 degree stem for a +6 degree stem, both being 90mm C-C, how much vertical drop in the handlebar height can I expect?

I think it's basic trigonometry using the law of cosines, but it's been a long time and I can't for the life of me remember how to figure it out!
Easiest way is the graphical approach:

http://www.habcycles.com/fitting.html

Analytically, the vertical rise of a stem is the extension length times the sine of the angle from horizontal:

Rise = Length x Sine( Angle from horizontal)

The ange from horizontal depends on both the angle of the stem itself, and the angle of the head tube:

Angle from horizontal = ( 90 deg. - Head Angle ) - Angle of stem

(Head angle is measured the traditional way, i.e. angle from horizontal. Angle of stem is measured from perpendicular to the quill or steerer clamp, i.e. a right angle stem would be 0 degrees.)

Assuming a typical 73 degree head angle, a +17 degree 90 mm stem would have a rise of:

Rise = (90 mm) x Sine( ( 90 deg. - 73 deg. ) + 17 deg. ) = (90 mm) x Sine( 34 deg.) = 50.3 mm

A +6 degree 90mm stem would have rise of:

Rise = (90 mm) x Sine( ( 90 deg. - 73 deg. ) + 6 deg. ) = (90 mm) x Sine( 23 deg.) = 35.2 mm

The net change in rise wouldbe 50.3 mm - 35.2 mm = -15.1 mm, or about 15 mm lower.

#### bikeboy389

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"Math savvy" is not congruent to "Bikeboy389."

But I do know that there's a site on the web somewhere with an Excel-based calculator you can download. You might be able to Google "stem height calculator" and find it. It's very handy, and will give you a graphical representation as well as the change in dimensions. You can also model changes in handlebar measurements with it, I believe.

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