# Optical Forums > Ophthalmic Optics >  lens thickness formula

## hip chic

Help!
A few weeks ago, I attended a seminar and jotted down a formula for determining lens thickness.  I suspect I wrote something incorrectly as I am not coming up with logical answers.  Does anyone know of a formula.  In the formula I was given, I had to take in to account Index of Refraction, Decentration, RX, Radius and Center Thickness (if a minus lens) or Edge Thickness (if a plus lens).  I thought it was a great formula because these are all variables that I would know at the time of order (having to know curves and sag. values ect. would NOT work).
I hope someone can help.  I appreciate the feedback.

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## Steve Machol

This really belongs in the Ophthalmic Optics Forum so I'm moving it there.

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OptiBoard Administrator

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## David Wilson

First, work out the lens diameter required (minimum size uncut):
MSU = ED + (2 X decentration)
Where ED is the effective diameter. That is, twice the distance from the lens center to the furthest point. It is often incorrectly referred to as the longest axis.
Now, work out the radii of the surfaces:

r1 = (n - 1)1000/F1
r2 = (1 - n)1000/F2

where F1 and F2 are the front and back surfaces, respectively (Americans often refer to them as D1 and D2)
(F2 will be negative, as will 1-n, giving a positive value for s2. Both sags will be positive figures)

Now work out the sags:
s1 = r1 - square root of r1 squared - y squared

s2 = r2 - square root of r2 squared - y squared
Where y is half the lens diameter (that is, half the MSU)

Finally, for minus meniscus lenses:

e = s2 - s1 + t
where e is the edge thickness and t the given center thickness

and for plus meniscus lenses:
t = s1 - s2 + e
where t is the center thickness and e the given edge thickness.

For toric lenses you will need to consider the meridional powers.
Sorry about the lack of math symbols (square root etc). I can work out how to do them in this format.
I hope that this helps.

Regards
David Wilson

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## Darryl Meister

David has given the exact thickness formulas for a given blank size (what he referred to as the MSU). If you have the time, these will give you a very accurate idea of lens thickness for non-aspheric/non-progressive lenses; assuming that you use the correct value of the MSU, which may not be so straightforward. (Also remember that lens thickness will vary as a factor of frame shape, cylinder power, prism, etcetera.) There is also an approximate formula that works particularly well for smaller frame sizes, and is a little easier to use when working with a patient:

Thickness = (1/2*Diameter)^2*Power / [2000*(Index - 1)]

Once you have calculated the thickness of the lens for a given blank size (Diameter), lens power (Power), and refractive index (Index), simply add the minimum thickness of the lens blank to your answer. The minimum thickness, which is usually the center thickness of minus lenses and the edge thickness of plus lenses, will generally be around 1.5 to 2.0 mm.

For instance, given a lens power of -4.00 D, a refractive index of 1.600, and a minimum blank size of 65 mm, the thickness would be:

(1/2*65)^2*4.00 / [2000*(1.600 - 1)] = 3.5 mm

Now, add 1.5 mm for the minimum thickness to arrive at a total "approximate" thickness of 5.0 mm.

I also have an article in the "Downloads" section on estimating lens thickness, which goes into some more detail. You might want to check it out sometime.

Best regards,
Darryl

Oops, got my minimum thickness values reversed! That's what you get for doing this stuff at 2:30 in the morning!

[This message has been edited by Darryl Meister (edited 01-19-2001).]

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## Steve Machol

What I'd like to know is why is Darryl up at 2:45 in the morning working on this stuff?!?

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OptiBoard Administrator

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## hip chic

WOW!!!!
Thanks so much for ALL the feedback.  I DID write the formula wrong.  You were a great help and this web site has a new fan.
Thanks again,
hipchic

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## Darryl Meister

> Originally posted by Steve Machol:
> _What I'd like to know is why is Darryl up at 2:45 in the morning working on this stuff?!?
> 
> _


'Cause the "freaks come out at night," Steve...  ;)

Best regards,
Darryl

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## Optom

Effective Diameter and Boxed Lens Size is one and same thing?? Can someone please clear my enquiry.My understanding is ED is american and BOXED LENS SIZE is british.

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## Maria

I would agree with that, since I've used BLS, but not ED. They change it a lot, though, so it's hard to keep up.

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## David Wilson

Shabbir,
Boxed lens size and ED are not the same thing. Boxed lens size is the width of the box enclosing the lens. This is often referred to as the A measurement, with depth of the box being the B measurement. Effective diameter (ED) is double the distance from the geometric centre to the furthest point on the lens. In most lenses this 'furthest point' will not be on the horizontal centre line (datum). So ED will always be larger than the boxed lens size (except on rare cases such as round shapes and prolate elliptical shapes).
A common error in calculating the MSU (blank size) is using the "longest axis", which is the distance across the widest part of the lens, instead of the effetive diameter. Only the ED will give you the correct blank size (although the longest axis will come close).
Incidentally, Shabbir, the boxing system is now the internationally accepted frame measurement sytem; it is not just British. The ISO have included it in their standards, as have ANSI and we Aussies among others. There are still a few variations of terminology, though, at least in general usage. What we call the horizontal centre line, Americans call the horizontal lens bisector. (If they did use the same term as us they would spell centre as center!)

Regards
David Wilson

[This message has been edited by David Wilson (edited 01-20-2001).]

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## Maria

Apparently now,ABDO have to move away from American terminology, and towards European guidelines. (A move welcomed by no-one). So now we are being taught different terminology. The datum line no longer exists, ABBE values are gone, etc etc. Which is great for me in the classroom, as I learn it in the 'language' I'm expected to use it. Until I arrive back at work, and of course the whole of optics still uses the old stuff. Which is just yet another reason why we should stay out of Europe.

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## David Wilson

Maria,
I'm not sure that we should heap too much blame on the Europeans. While the International Organization for Standardisation (ISO) is located in Europe, its members include, the United States, Australia and, of course, the UK. The reason for the demise of datum as a term, I suspect, is that it might cause confusion of the old system (the datum system) and the new, internationally accepted, system (the boxing system). Since the horizontal centre line (HCL) is the same animal as the old datum I suspect that most of us will continue to use the term 'datum'. I agree, though, that it would be nice if we tidied up our terminology, which I think is one of ISO's main aims. We may not like all of their decisions but their motives are laudable.
Life is not entirely a bed of roses in ISO, though. There is a continuing debate about which should be the accepted reference wavelength, the helium d line, used by the USA, UK and Australia (among others) and the mercury e line, used by the European manufacturers.
Regards
David Wilson

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## Maria

All bad things are the fault of Europe. Never ever forget that. Ever. Or else.

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## Darryl Meister

Hi David/Maria,

We Americans haven't actually used the "datum system" for a very long time now... We've been using the "boxing system," although we do still occasionally refer to the horizontal (or geometric) center line as the "datum line." (This was the actually the same reference line in both systems.) I believe that the Britts, on the other hand, had to deal with "datum lengths" and "datum centers" up until quite recently, since the British Standard used to employ the official "datum system."

Please keep in mind that, while America and other countries belong to the ISO, we get a fraction of the votes that the E.C. does (what I lovingly call the European Country).   ;)

Best regards,
Darryl

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## Optom

Thank you all for your contribution,but I am still convinced that ED and BLS is same.When we measure lens size using boxing system we are actually measuring effective diameter of the lens.
Yes,datum line is different from horizontal centre line(HCL).
I request more opticians to come forward to discuss on this issue.

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## shanbaum

> Originally posted by SHABBIR KAPASI:
> _Thank you all for your contribution,but I am still convinced that ED and BLS is same.When we measure lens size using boxing system we are actually measuring effective diameter of the lens.
> Yes,datum line is different from horizontal centre line(HCL).
> I request more opticians to come forward to discuss on this issue._


1.  ED = twice the longest radius from the box center of the shape to the edge.

2.  BLS = the width of the bounding rectangle, the sides of which intersect the shape at its furthest protrusions along the major axes.

Perhaps it would help alleviate your confusion to visualize a circle inscribed within a box.  In the case of a circle, the ED, A (horizontal box), and B (vertical box) dimensions are all the same.  Now, grab the circle at the lower left-hand corner, and pull it slightly towards the lower left-hand corner of the box - say, 1mm.  You've just made the ED 2mm greater than the A and B dimensions, without changing either of those.

Does that help?  Or do you disagree with my definitions?  In that case, explain in what way you disagree.

The "horizontal centre line" is the same as the "datum line" - it's the horizontal line that bisects the B dimension.  I haven't heard the former expression used in the U.S.; and, David, to my knowledge, no-one currently residing in the U.S. has _ever_ uttered the phrase "horizontal lens bisector" (which would probably be illegal in parts of the South, anyway). Everyone calls it "the datum line".

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## Maria

When measuring for varifocals, do you do it "heights from the bottom of the frame" or "distance from datum"?

Edit - spelt varifocal wrong, because I'm eating and typing at the same time  :)

[This message has been edited by Maria (edited 01-25-2001).]

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## shanbaum

> Originally posted by Maria:
> _When measuring for varifocals, do you do it "heights from the bottom of the frame" or "distance from datum"?
> _


I'd argue that the bottom of the frame - the base of the boxing rectangle - is the only reference point from which you _can_ measure.  You can see it, which is not true of the datum line; how likely are you to measure accurately from a point you can't see?

Of course, you can measure a height and convert that to a drop ("distance from datum"), but doing so doubles the odds you'll err - in locating one side or the other of the "B" dimension whilst determining that.

Notice I wrote "whilst"?  How fab is that?

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## David Wilson

Shanbaum,
Thanks for putting me straight on the horizontal lens bisector. I'm sure that no one utters it now but I did read it in an American publication. I'll have a hunt around and see if I can find it. Incidentally, I like your explanation of the ED with the distorted circle.
Maria, I hate to be pedantic (actually that's not true, I like to be pedantic) but the ISO standard now uses the term progressives rather than varifocals (as does the British standard, I believe). Mind you that wont stop British opticians calling them varifocals or Australian opticians calling them multifocals (which is much worse in my view). Habits are hard to shake.
Regards
David Wilson

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## Maria

Shanbaum - I get a lot of safetyspec orders where our store fills in the Rx and measurements, and another company entirely makes them, then we fit them. As such, we are nothing to do with the design of the order form. And some of them ask for the heights in relation to the datum line, which is highly annoying. I assume I'm supposed to mark the position on the dummy lens, then measure the datum line, draw that on, and measure the difference. But for a £16 dispensing fee, I just cross out the datum bit and write 'heights' in.  :)If they paid us more, then perhaps I would go to the trouble of doing it their way. But until then, it's tough.
I much admired your grammar, by the way. It was lovely.
David - if you like to be pedantic, look back at my old postings, you'll find enough to keep you happy all day. As far as the term 'progressives' goes, here's some real pedantry for you.
I have studied English Language, and in particular the way new words come into being. And basically, when a word is used by a lot of people, it becomes part of the offical language. For example, this is how words pertaining to the internet have entered the language. On the day that someone thought "I know, we'll call transferring files 'downloading' them", downloading wasn't a real word, but now that it is in common usage, it gets to be in the dictionary and everything.
And now for the point of this diatribe!
All our company literature, our training packages, our supply labs, our staff and *customers use the term 'varifocals'. The only person who uses the term 'progressive' is a lens rep who once did a talk/intensive sales pitch at the store.
Therefore, under the conventions of the structure of the English language, 'varifocal' is an accepted term, being in common usage, and 'progressive' is a minority word, belonging to the strange patois of lens reps.
And I win again  :)

*An exception has to be made for those customers who call them 'bifocals without lines'. They are just halfwits.

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## Optom

We use term PPL(progressive powered lenses)and when it comes to heights we give in reference to HCL(horizontal centre line)e.g. 2mm below HCL or 4mm above HCL.A ?? true boxing system!
Well friends,this system works very well in my office.

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## Optom

Maria-I guess the word VARIFOCAL came into use from an exclusive brand name VARILUX,progressives from Essilor France.But I am not certain.

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## David Wilson

Maria,
I take your point about usage. This is why multifocals has become the term of preference for many Aussie opticians and optometrists, despite the fact that the Australian Standards in a, perhaps vain, attempt to correct this 'error' of usage states that "A progressive lens is not a multifocal". Varifocal is a better and more accurate term for this animal, I grant you, and it is the only term to appear in the index of Jalie's seminal work, "Principles of Ophthalmic Lenses", but you will find that your own standards dismisses 'varifocals' as a deprecated term. I suspect that the reason for the apparent pedantry on the part of Standards Australia, the British Standards, ANSI and ISO (and me)is to get us all to speak the same technical language. Alas, it seems that it is a folorn hope.
By the way, Shanbaum, I found the source of my belief that Americans use the term Horizontal Lens Bisector. In the recently published Dictionary of Ophthalmic Optics by Keeney, Hagman and Fratello, they have an entry under HLB where they say that the equivalent terms, datum and horizontal centre line are lesser used or obsolete.
I'll finish here with a quote from the abovementioned dictionary's preface that warms the heart of a practising pedant. "Shop jargon and abbreviated expressions will alwats be part of personal interchange, but accomplishing growth of science and scientific interchange is dependent upon clarity of definition." And, yea, Maria, there is also a quote for you, "Dictionaries are living and unending creations."
Regards
David Wilson

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## Optom

DATUM LINE:
Datum line system was introduced by Cole & Blackburn in 1935.The datum line is situated midway between the horizontal tangents to the upper and lower edge of the lens shape(no vertical tangents mentioned).This system was enshrined in BS 3199 of 1960.However,with the introduction of BS 3521 in 1991,datum system ceased to be used in United Kingdom replaced by boxed system.Most countries now use boxed lens system,and it is most likely that this system will be universal.
BOXING SYSTEM:
It was American Optical Manufacturers Association in the year 1961 introduced Boxing System for Lens and Frame measurements
This system is based on the rectangle formed by the horizontal and vertical lines(vertical line is mentioned here,but not in datum system)tangential to the  extremes of each lens,by which dimension of a front(I don't use term frame)and the location of the lenses in the front may be measured.
Accordingly,HCL should be used for centration purposes and to specify the segment top position(height)and the fitting cross height.
Again I say,effective diameter=boxed lens size,because both are the one and the same boxing system!
Therefore,Boxing System is improved version of Datum System

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## David Wilson

Shabbir,
I'm sorry, but the effective diameter is definately not the same as the boxed lens size. Shanbaum expressed it rather well in his example. It is the distance from the geometric centre to the furthest point, doubled. It will only equal the boxed lens size in a round shape or a prolate elliptical shape. The boxed lens size is the distance between the two vertical tangents to the lens (or the distance from the gometric centre to either vertical tangent doubled. The ED will always be larger (except in the two cases I mentioned).
Let me quote from the dictionary I mentioned in an earlier post. Effective diameter is "A linear measurement expressed in millimeters, equal to twice the distance of a radius measured from the geometric center to the farthest finished apex edge of an ophthalmic lens."
I'll also give you the definition I used in my book. Effective diameter is "The distance from the geometric centre of the lens to the furthest point doubled."

The farthest point is rarely the vertical tangent, indeed it is only the vertical tangent in the two cases I mentioned.
Regards
David Wilson

Shabbir, on re-reading your last post, particularly the comment that the boxing system was an improved version of the datum system, I now think that you may have assumed that the boxing system is just the datum system with new terms. They are quite different systems. The only thing they share (but with different names) are the datum line or HCL). The lens size under datum is the distance between the peaks of the bevel on the datum line, whereas the lens size under boxing is the distance between the vertical tangents to the lens. The 'bridge sizes' are also different. Have a look at an aviator shape to see the full effects of the differences in the systems.So, if we had an aviator frame we might find that the datum frame size is 54-16 while the boxing size might be 56[]12. You will note that the geometric centre distance, or 'frame PD" as many call, is larger for the datum measurement (with an aviator frame).
[This message has been edited by David Wilson (edited 01-27-2001).]


[This message has been edited by David Wilson (edited 01-27-2001).]

[This message has been edited by David Wilson (edited 01-28-2001).]

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## Optom

David,
All explanations are good and I will sit with opticians at my office to further learn dispensing optics.
A good reason to join you folks.
Thanks again dear all.

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## Alan W

You guys . . . . are so smart. It scares me. I mean . . where did all this smart come from? It sure ain't on the general forum!
Now, I'm just a country boy with a degree here and there . . . but I always used a simple rule of thumb for the ED. Until recently I considered ED to be Estimated Diagonal measurement with the understanding that it would with only a couple exceptions, be the longest measurement of a lens. A hypotenuse of sorts. However, in modern times ED now seems to be confused with  . . . nahhh . . . I won't say it!
Ask Bob Dole!

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## CJ Engel

I agree with David on this subject. You are 100% spot on with every statement you made here David. That’s probable the reason you are in Charge of training of half the good Opticians out there. Good work David.

As far as the VARIFOCAL’S I would agree that it originated from the VARILUX brand. Essilor runs the Varilux University and just for the record in their entire fitting guide for fit VARILUX lenses they refer to them as (PROGRESSIVE LENSES). So I am guessing that the internationally recognised term (PROGRESSIVE LENS) now speaks for itself. In South-Africa the majority of us use the “progressive” term. Maybe one or two very old optoms will use multifocal or varifocal. Maybe its an age related thing Maria? =)

Regards 
CJ

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## Speed

Most formulas calculate for 0 ct or et.  Make sure you are adding those somewhere.

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## Fezz

****9 year old thread revival ALERT****

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