In Lesson 1 of this course, you learned about the lens index. In this lesson you will learn about another property of lenses called the base curve.

Remember that to fully understand the concepts covered in this lesson, it is best to have read through the entire The Optics of Vision course.

The True Shape of Lenses

Up until now, I have been simplifying the shape of lenses in order to make obvious the distinction between plus and minus lenses.

Here is the shape of lenses that you are use to seeing:

A Convex Lens A Concave Lens
A Plus Lens A Minus Lens

Here is a more realistic depiction what these lenses look like when they are manufactured for glasses:

Ophthalmic Plus Lens Ophthalmic Minus Lens
A Plus Lens A Minus Lens

Quite different, right? But don’t worry, it’s still very simple. Let’s break it down.

The Front and Back Curve

Every lens has a front and a back surface curvature. The front curvature is always convex and the back curvature is concave.

A lens with a flat back curve

The Lens Power

The overall lens power is simply the sum of the front and back curvature.


  • The front curve is always positive
  • The back curve is always negative

In order to do this you must be comfortable with adding positive and negative numbers.

For example, here an example of a +2.00 lens.

Front and Back Curve

This is a +2.00 lens because the front curve is +6.00 and back curve is -4.00. If you sum these together, you get +2.00.

+6.00 + (-4.00) = +2.00

What is the Base Curve?

In practice, we call the front curve the base curve.

Now, of course there are several different ways to combine base (front) curves and back curves in order to arrive a +2.00 lens.

Other options would be:

Base Curve Back Curve
+2.00 0.00
+3.00 -1.00
+4.00 -2.00
+5.00 -3.00

But as it turns out, only specific combinations of base curves and back curves are used for any given desired lens power.  The goal is to create a lens that is as comfortable as possible to see through by using the most appropriate combination of base and back curves.

For Example, the following lenses are both +2.00 lenses, but one has a base curve of +6.00 while the other has a base curve of +12.00. Which one would you rather have in your glasses?

Two Different Base Curves Examples

Obviously, the lens with the +6.00 base curve is much more desirable.

How To Determine The Optimal Base Curve

The most optimal base curve for any prescription  can be calculated using these equations:

For Plus Prescriptions

Base Curve = Spherical Equivalent + 6.00

For Minus Prescriptions

Base Curve = [ 1/2 * (Spherical Equivalent) ] + 6.00 

No worries though, as with everything else we don’t actually work with formulas. We make charts.

This is a simple base curve selection chart. Note: This chart does not apply to all lens indexes and lens designs.

Base Curve Selection Chart

There are many reasons why base curves have to be carefully selected for the strength of each prescription. Here are just a few:

The wrong base curve can…

  • cause unnecessary distortions in vision
  • cause inability to adapt to a new prescription
  • cause lenses to be thicker than they need be

How To Measure The Base Curve?

The base curve of any lens can be measured with a tool called  a radius gauge, also known as a lens clock.

Lens Clock

A lens clock has three prongs that can measure the curvature of lenses (and other surfaces).

When those 3 prongs are place against a flat surface, the gauge should read zero. The following image shows a lens clock held against a flat counter top.

Lens Clock on Flat Surface
A lens clock read zero (more or less) when held up to a flat surface.

When a lens clock is held up against a convex surface, the black numbers indicate the curvature of that surface.

Lens Clock Measuring Base Curve of Semi Finished Lens
A lens clock measuring a +5.00 front/base curvature.

When a lens clock is held up against a concave surface, the red numbers indicate the curvature of that surface.

Lens Clock Measuring Back Curve of Semi Finished Lens
A lens clock measuring -2.00 back curvature.

In the example above, the base curve is +5.00 and the back curve is -2.00. Hence, this lens has an overall power of +3.00 (+5.00 + -2.00).

The same can be done on lenses already mounted into glasses.

Lens Clock on Measuring Base Curve Lens Clock Measuring Back Curve

The process I’ve illustrated here is somewhat simplified and assumes there is only Sphere power in the lenses. In reality, many lenses you encounter will have both Sphere and Cylinder power. It is rare to use a lens clock to determine the cylinder power of glasses, but if you’re interested in learning more about that, click here.

Who Deals With Base Curve?

Optometrists do not write down the base curve on their patient’s prescriptions, so does it fall upon the optician to order the correct base curve? Yes, most of time.

Despite how critical the correct base curve is to the overall finished pair of glasses, it is not typically the biggest concern when dispensing glasses. In most optical stores, the customer’s lens order is sent to a lens manufacturing laboratory who’s skilled technicians select the most appropriate base curve for every lens order.

Of course, if a specific base curve is required, the optometrist or optician can specify this on the prescription/lens order. Often times when the base curve is specified, it is done so in order to match the base of curve of the lenses in the customer’s old glasses.

Quiz Header

Case Scenario:

A customer gets her eye exam and it is determined that her prescription has not changed at all since she got her last pair of glasses. Even though her current glasses are still in good shape, she decides to get new glasses anyway. You make her new glasses with the exact same prescription as her old glasses. The customer returns to the store one week later saying that she can’t see as well with her new glasses as with her old ones.

What could be the problem?

Possibility #1

It could be the base curve. Using a lens clock, measure the base curve of the old and the new pair of glasses. If the base curves are different between the two pairs, it could be very difficult for the customer to adapt to the new glasses (even though the prescriptions are exactly the same).

Possibility #2

If the base curves are the same between the two pairs, another possibility could be incorrect PD (pupillary distance) and OC (ocular center) height measurements.

If you don’t know what a PD and an OC height are, that’s because I haven’t taught it to it you yet, but that is the topic of the next lesson!

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