What Does “Axis 180” on a Toric Lens Box Mean?

Turn a box of toric lenses around and you will find the number 180 next to the power. On a family member's box, the same spot says 90. Does twice the number mean twice the astigmatism? Or has a unit been left out?

Axis 180 is a number for direction, not for the strength of astigmatism, and it shows that the reference line lies horizontally. Imagine a protractor standing in front of your eye, with this number as one mark on its scale.

How lenses are designed not to rotate on the eye is covered in Why a Lens for Astigmatism Must Never Spin on Your Eye. This time we look only at how the number is written, in other words the angle notation itself.

180 is a direction, not a strength

The astigmatism numbers in a prescription come as a pair. Cylinder (CYL) is the size of the correction, and axis (AXIS) is the direction in which that correction lies. Refraction teaching material from the University of Iowa's ophthalmology department explains that the axis sets the direction of the cylinder power, and notes that in astigmatism the two powers always lie 90 degrees apart.

So if the axis is horizontal, at 180, the side where astigmatic correction is added is the vertical direction at right angles to it. The size of the number has nothing to do with strength. 180 is not stronger than 90. As numbers, 10 and 170 are 160 apart, but as lines they are only 20 degrees apart, one on either side of the horizontal.

If you would like to look at the other boxes on your prescription as well, Six Codes Hidden on One Sheet of Paper may help.

How does the protractor sit in front of the eye?

This protractor has a name. The terminology dictionary of Quebec's language office in Canada describes “Tabo notation”, named by abbreviating the title of a German body, as the most widely used system today. The international standard ISO 8429 sets out the same coordinates. The reference line is horizontal, angles increase anticlockwise and 90 degrees is vertical. These coordinates are defined from the viewpoint of someone outside the eye, facing the wearer.

It also matters that the right and left eyes use the same coordinates. Angles are not measured from the nose side or the ear side. The Iowa material likewise explains that the patient's left is 0 degrees for both eyes.

So axis 45 is a line rising to the upper right as seen by the examiner. Picture it from the wearer's own viewpoint and left and right flip, so trying to work out the direction in your head from the box number alone easily becomes confusing.

Why 180 rather than 360?

A clock's hand means different things at 12 and at 6, because its tip points one way. An axis is a straight line, not an arrow. Turn a line half a circle and it looks the same as when it started, so every direction can be shown within 180 degrees.

The standard makes this distinction too. ISO 8429 specifies cylinder axes as numbers from 0 to 180 degrees and prism base directions as numbers from 0 to 360 degrees. With a prism, the way the thick side faces has meaning, so it needs the full circle, like an arrow.

If 180 and 0 are the same line, why 180?

You can call the right end of the horizontal line 0 and the left end 180, but they are one line. The Iowa material also calls the horizontal direction the “0 and 180 axis”. And it says plainly that when the correction direction is horizontal, it is recorded as 180, not 000.

The standard's range also includes 0, so on the wording alone the two seem slightly at odds. One way to read them is that the standard sets the range of numbers, while the teaching material shows how the horizontal is actually recorded. It is hard to find a source that goes as far as explaining why 180 came to be used rather than 0.

Why is there no degree sign after the number?

In a prescription record, the axis is the last number after the x. The Iowa examples also use numbers alone, such as 078 and 005, and advise writing three digits, such as 012 instead of 12.

Leaving out the sign is a convention, not a rule. The standard's wording mentioned above keeps the sign, as in 0° and 180°, and it is hard to find any document officially explaining why it came to be dropped from prescription records.

A useful example comes from medical records. The US ISMP's list of error-prone abbreviations warns that the ° sign meaning hours can be misread as 0, giving the example of q2° being read as q20. That concerns medication records, so it is not a rule that applies directly to lens axes. It does, however, show the risk of one small circle being read as a number.

Why are 10-degree steps so common?

A 2006 article in Contact Lens Spectrum stated that most disposable soft toric lenses come in 10-degree axis steps. Rising through 10, 20 and 30 to 180 gives 18 slots.

It is hard to find a direct explanation from manufacturers of why 10 degrees, but the size of the acceptable error offers a clue. A 1996 design proposal in the same magazine explains that a toric lens 10 degrees out of position shows up as residual astigmatism equal to one-third of the cylinder power, and that most people tolerate anything below that. The author proposed making low cylinder powers in 10-degree steps and high powers in 5-degree steps.

The number of slots can be considered alongside this. Narrow the axis to 5-degree steps and 18 slots become 36, doubling the number of product types even if every other specification stays the same. The same article also wrote that keeping to a single diameter reduces the burden on stock and production.

When the prescription axis and the box axis differ

Axes on glasses prescriptions can also be written to the single degree, as in 078 or 005. A lens made in 10-degree steps cannot simply take over that number. The 2006 article explains that soft toric lenses tend to rotate 5–10 degrees towards the nose, and that because they can only be ordered in 10-degree steps, rotation has to be allowed for as well.

So the axis on the box may differ from the number on your prescription or your glasses. Which value is right is for a professional who has seen the lens on your eye to judge, so if the numbers look different, it is best to check with an ophthalmologist or optometrist.

Next time you look at a box, draw the axis number with your finger. For 180 draw a horizontal line, for 90 a vertical one, and for anything else a line somewhere in between. A number that looked like a size turns into a direction right in front of your eyes.