Meridian Power Calculator



I’d like to introduce EyeDock’s newest optics calculator, the Meridian Power Calculator. This calculator will - you guessed it - calculate the powers of a pair of lenses in a specified meridian.


How Do I Use It?

I tried to make the calculator as simple as possible, so hopefully it’s fairly self-explanatory: 


  1. Type in the spectacle Rx for each eye

  2. Drag the meridian selector to whichever meridian you’re interested in. 

  3. Or, use the buttons below the calculator to go to a common meridian. 


See the Why Should I Care About Meridian Powers? section below for more explanation about the buttons.


How Are Meridan Powers Calculated?

Calculating the power in a specific lens meridian is not particularly difficult if you remember the formula:


 Dc´= Ds + Dc (sin² θ)



  • Ds is the sphere component of the Rx

  • Dc is the cylindrical power

  • θ is the difference between the axis of the Rx and the meridian in question


If you can’t remember the magic formula (and for some reason you don’t have access to EyeDock!), you can come up with a pretty good estimate for the lens power in a specific meridian just based on how far away your desired meridian is from the axis. 

I’ve written a blog post with further discussion about meridian calculations and estimations here: Discussing Meridian Power Calculations.


Why Should I Care About Meridian Powers?

When we write a glasses or contact lens prescription we use a format that allows us to describe the power in the primary meridians (the weakest and strongest meridians), and the angles of those meridians. The vast majority of the time this gives us all the information we need to know about a lens.

However, there are times where it is useful to know the power in a meridian that is not a primary meridian. 

 The most common situation is when you want to calculate the prism induced by looking through a decentered lens. If your patient is wearing a pair of glasses where the PD is off by 5mm, how much prism is being induced? 


To calculate this we use Prentice’s Rule (I’ll talk more about Prentice’s Rule in another post), which takes into account the lens decentration and the power in the meridian that the lens is decentered in. If we need to calculate the prism induced by a lens being decentered because of an incorrect PD we are going to want to know the power in the horizontal meridian, or meridian 180º.

Similarly, we may also want to know the power in the vertical meridian (at 90º). This can be helpful for calculating induced prism while in downgaze. This can be particularly problematic when we're dealing with a glasses prescription that has a significant power difference (anisometropia) between the right and left eye, which can result in image jump while in downgaze (for example, when looking through a bifocal). If the right and left eye powers are too different in the vertical meridian slab off prism may be necessary.

However, the above scenarios were not the reasons for building this calculator. To be honest, determining power in the 180º and the 90º meridians is not very difficult to calculate or at least estimate.

Instead, the catalyst for this calculator came from Daniel Deligio, O.D., FAAO, of Midwestern Univerisity, who contacted me with an interesting problem.  

. . . To give you some background, some insurances do not cover medically necessary contact lenses [MNCLs] unless there is 3D or greater difference between the two eyes in any meridian. This can be difficult to calculate if the Rx is not similar between the two eyes. Being frustrated with this, I created an excel document that I can enter SpecRx's into and it will tell me what the power is in every meridian and what the difference is between the two eyes to see if I can submit for MNCLs.

In other words, insurances (such as EyeMed and Davis Vision) will consider contact lenses medically necessary if the patient’s spectacle Rx contains anisometropia exceeding 3D in meridian powers. 

This is a trickier problem: We might know how to calculate the power in a specific meridian, but when determining if lenses are medically necessary we might be a little unclear on which meridian is the most different. For example, consider this Rx:

OD -2.00 -3.00 x 140

OS -1.50 -2.00 x 025


On the surface, the eyes look pretty similar: A bit of myopia with a moderate amount of astigmatism. Is there more than a 3.00 D in any meridian? It’s hard to tell at a glance, isn’t it?

This calculator will help answer this question: Just enter your Rx and hit the “Greatest Power Difference” button. As it turns out, the greatest power difference is at meridian 40º and yes, the power difference is more than 3.00 D!