Using Bar XY Cartesian Coordinates

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.

Diagram of XY on bicycle

This set of metrics was first espoused by Dan Empfield (founder of Quintana Roo bikes and 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.

Difference in stack and reach between 2 frames

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

Definition of Bar XY diagram

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:

Our 3D Motion system digitally captures both Frame XY and Bar XY.

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.

Bar XY calculation illustration from SlowTwitch
Ways to use our system

One easy way to calculate Bar XY if you don’t have a tool (and you’re working with a reasonably modern bike) is to enter the details into Frame Comparison and have the system do the calculation for you. From there you can enter the values into the Advanced System.

If you prefer to search by Frame XY (Reach and Stack) - perhaps if you’re using a Fit Bike that allows the fitment of a normal Stem - you will need to measure the Bar XY first.

Then in the Advanced Options of the Advanced System, select the “Preferred stem length” as shown below.

Preferred stem length setting in Advanced Bike Finder

This method narrows down the viable Frame XY options to a small range.

See also: