I received the following email from Eli today:

*I have a question about your vertex calculator. If I try to vertex correct a refraction of -9.00-2.00x180, the diagram of the power cross that comes up on your website shows -8.00 in one meridian and -9.75 in the other meridian (a cylinder amount of -1.75), but the vertexed prescription is listed with -1.50 cylinder. It just seems like there is a discrepancy between your diagram and the vertexed prescription written just below it. Thanks for your help in understanding this.*

This question pops up every once and a while, and it’s a good one. This looks like a mistake, or at least a discrepancy, but it’s really simply a phenomena of rounding.

If you take the -11.00 D meridian and vertex it, the actual value you get is -9.72. However, I like the optical cross labels to look nice and tidy, so I wrote the program to round this up to the nearest quarter diopter, -9.75.

Similarly, the -9.00 D meridian ends up vertexing to -8.12. This gets rounded to -8.00 (but just barely - if it was more than -8.125 it would have been rounded to -8.25).

As a consequence, one meridian was rounded up to -9.75 and the other rounded down to -8.00, so the optical cross seems to show a -1.75 D cyl power.

However, the suggested cyl power uses the true calculated values, -9.72 and -8.12, and subtracts them to get the cyl power, which turns out to be -1.60 D in this case. Because I still wanted things to look pretty - and to be easier to compare to our real world contact lens options - this is rounded to 1.50 D.

In summary, when you see a discrepancy between the cylinder on the optical cross and the cylinder on the suggested Rx, the true, *exact* number rests somewhere between these values. However, rest assured that the cylinder in the suggested Rx will always be within an 1/8 D of the exact calculated power.

I hope that makes sense!

-Todd