79pmooney

The cheap approach I would try. Get a ruler and protractor. (You might have to go to a store with school supplies and spend $5.) Draw a line on the paper 72 degrees from horizontal, This is the angle of the fork, headtube and steerer. Put a mark on that line that indicates the bottom of the spacers under the stem. Another at the top of those spacers. Now draw in your existing stem above the spacers. If you know the angle and length of your current stem, draw that line through the handlebars and crossing the 72 degree line.

Go to your bike and place your hands where you want the bars to be and measure where that is relative to your current handlebar position, (1" up and 1/4" forward, say.) Place an "X" on your drawing there. Now draw a line from you new "X" to the crossing of your old lines. That is the stem you want; Now, that exact stem might not be available but you can get very close by adjusting the spacers and using slightly different angles.

I completely get that this approach is not in everybody's skill set. I'm an engineer type and seeing it on paper has always been both easy and enlightening. I went to school and went out into the field before computer drafting so problem solving required putting it on paper. Now I have AUTOCad and have all my bikes overlaid on each other. When I buy a bike, I go measure the key points, draw it up that night, and see whet I need for stem and seatpost to get that bike to fit me. Only then do I decide if that is a bike I want.

Fit is serious stuff. The right fit will make that bike feel sublime (assuming the bike works well, rolls nicely, etc). There is no exclusive way to find that right fit. A fitter can (and should) get you close but it is not guaranteed, Trial and error can. But with trial and error, documenting what you have done can save you years and dollars. Drawings can be very valuable later and when you want to make changes or get a new bike.

Edit: I said 72 degrees for that first line. Headtube angles vary from 70 to 75 degrees. If you know yours, use that, But a 2 degree error in headtube angle will make almost no difference in the distances we are talking here.