Using Bar XY Cartesian Coordinates

Complete guide to using Bar XY Cartesian coordinates for bike fitting and frame comparison. Learn about Reach and Stack metrics and why Bar XY provides more accurate frame sizing.

Over the last few years it has become standard practice for bike manufacturers to provide Reach and Stack figures in their geometry charts. As shown below, these metrics give the coordinates of the top of the Head Tube relative to the Bottom Bracket.

Reach and Stack diagram showing measurements from bottom bracket to head tube

This set of metrics was first espoused by Dan Empfield (founder of Quintana Roo bikes and slowtwitch.com) and rapidly adopted by a few, mostly Tri-focussed, brands.

Wide acceptance has taken 10 years but it is now rare not to be given these metrics, which is of great benefit to bike fitters.

Reach and Stack precisely define the size of the frame, compared to Top Tube Length which is an imprecise measure of the length of the frame as it is modified by the Seat Tube Angle.

The example below (from our Frame Comparison tool) demonstrates this effect. The Cervelo R5Ca was built with a slack Seat Tube Angle (to enable the use of lighter Seat Posts) so has a 25mm longer Top Tube than a Felt Z-Series bike. But when we look at the Reach of the Frame there is only a 6mm difference.

Frame comparison showing effective top tube vs reach differences between Cervelo R5Ca and Felt Z-Series

Knowing Reach, Stack and Head Tube angle makes it easy to calculate the configuration of the Handlebars and compare the true size of different bikes.

However, the failing of using Reach and Stack to compare frames arises because of the slope of the Head Tube. The example at right demonstrates this effect.

The Reach of these two frames is very similar, which could make them look like they are the same size apart from needing different spacer heights to account for the large difference in Stack.

However – extra Stack has a negative impact on Reach (roughly a 3mm reduction in Reach for every 10mm Spacer).

Once we've added an extra 25mm of spacers (thus normalising the Stack of the Frames) the Litespeed turns out to be 9mm shorter Reach than the Felt.

By comparing Bar XY we are able to account for the dimensions of every component that connects the Handlebars to the bike.

This more precise calculation is why we offer the Frame Comparison tool for direct calculation, or the XY bike search in the Advanced Bike Finder (look under Advanced Options).

All results in our Advanced Bike Finder show Bar XY in the detailed specifications, regardless of which input method you use to define the bikes.

Definition of Bar XY

Bar XY coordinate system definition showing measurements from bottom bracket to handlebar center

Bar X and Bar Y are measured from the centre of the Bottom Bracket to the centre of the Handlebar.

There are tools available such as:

• Purely Custom XY

• Exitcycling Reference

Our Velogic Studio system digitally captures both Frame XY and Bar XY; see our docs on taking-bike-measurements.

How is Bar XY Calculated?

The traditional method is shown below. This method suffers from a systematic error that gets worse the more the stem is angled. At velogicfit we have a proprietary algorithm that more accurately calculates Bar XY, taking account of the effect of stem angle correctly.

Traditional Bar XY calculation method showing geometric relationships and stem angle effects

See also:

• Our free Frame Comparison tool

• Our free suite of Velogic Web Tools

• A guide to Using Frame Comparison

• Frame Comparison Bar Curve Analysis