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# Diopter to Radius Conversion for NCLE

The value of a contact lens base curve can be expressed in both millimeters of radius and diopters of power. Converting from one to the other is one of the basic skills opticians must master for contact lens fitting.  You also need to know it to pass the NCLE.  There will be questions on it directly, and questions in which diopter/radius conversion is one of several steps.

NCLE questions could take many different forms:

• Give the diopter value for the following radius value.
• Which of the following is the steepest/flattest base curve? (the answers will be mixed)
• Which of the diopter values is steeper/flatter than 8.3mm? (also mixed answers)
• If we increase/decrease a 8.3mm base curve by 0.15mm what would be the resulting diopter value?
• If the base curve you order is 8.3mm and the curve you get is 8.1, what is the difference in diopters?
• You order a CL with base curve 7.9, but it comes in 0.25D to steep.  That is the dioptric value of the received lens?
• Given the following K values, what is would be the base curve if fitted “on K”  (all the values are in millimeters.)
• What would be the intermediate curve of a lens of base curve 8.9mm. (all the values are in diopters.)

You get the idea.

## Conventional “Rules of Thumb” for Radius/Diopter Conversion.

All NCLE prep course and manuals contain a Diopter to Radius  conversion chart.  No one can possibly memorize this chart so there will be a formula, a “Rule of Thumb” for you to memorize.  It could be worded like this:

For every change of o.50 in base curve diopters there will be an approximate
change of 0.10mm in radius of curvature.

This is a rough “rule of thumb.”  It gives you an approximate value only.  And it all hinges on remembering that:

7.5mm  =  45.00 diopters

You base all your calculations on that.

So, supposing you get this question:

If the base curve measures 8.3mm what is the value in diopters?

The first thing we do here is to figure out the difference between 7.5 and 8.3 and then calculate how many 0.50 diopters you need to add to, or subtract from, (this is very important!) 45.00D to get your answer.  If you are going UP in radius, you need to go DOWN in diopters.  If you are going DOWN in radius, you need to go UP in diopters.

We are going UP in radius here, so we subtract from 45.00D.

8.3  –  7.5  =  0.8     which is 0.10 x 8    or 0.80  x  0.50  = 4.00D

45.00D  –  4.00D  =  41.00D

But that is only approximate. It is not a perfect answer.  The greater the value AWAY from the 7.5mm or 45.00D, the less accurate that “Rule of Thumb” will be.

But there is a much better way!

### Accurate Shortcut for Radius/Diopter Base Curve Conversion.

What if there was ONE number, one constant or value, that would accurately allow you to convert radius to diopters AND diopter to radius in one single calculation?

There is such a “magic number:”   337.5

It is all you need for radius conversion.

Just divide 337.5 by either the radius value OR the diopter value and you will get the answer you are looking for.

337.5  ÷  7.5mm  =  45.00 diopters
337.5  ÷  45.00D  =  7.5 millimeters

Going back to our example of 8.3mm let’s use the magic number.

337.5  ÷  8.3  =  40.662

This is the exact diopter value.  You don’t need to remember if you should add or subtract (though you should understand the concept!) There is one less step involved where you can make a careless error (which happens to the best of us!) and your list of answers will include ONE that fits your calculation.  40.662 could round down to 40.50 or it could round up to 41.00. But which one is more accurate?

337.5  ÷  8.2  =  41.15    over 41.00 but closer to it.
337.5  ÷  8.4  =  40.17   under 40.50 but closer to 40.00

40.662  would correspond more to 40.50 than 41.00

But if the best answer given is 41.00 that’s it!

#### Practice Essential for NCLE Preparation.

The more you review the material, the better you will do on the NCLE.  And the best way to review is to take practice tests.

At www.passyouropticalboards.com we have thousands of questions in our database, and each NCLE prep test you take will give you a unique selection of contact lens questions.  After you complete each test, you can review it over and over, and by pressing the Learn More button, you can read explanations of the right and wrong answers for all the questions in the test.  All the mathematical steps will be shown.

The more tests you take, the more you will learn!

Good Luck on your NCLE.  We want you to ACE it!