30-45-60 Rule

This rule allows us to calculate powers at an axis that is not conveniently located perfectly vertical (90 degrees) or horizontally (180 degrees). This comes in handy when we need to calculate the amount of prism in oblique meridians. When you need to calculate the amount of power a lens has 90 degrees away from the current axis all you have to do is flat transposition. For example;

-7.00 -1.00 090 is the same as -8.00 +1.00 180.

At no point will the lens power go lower than -7.00 (thinnest portion of the lenses) and at no point will it go above -8.00 (thickest portion of lenses). If your math is wrong, keep this in mind to double check your work. Your power should be somewhere between the lowest and highest possible powers (90 degrees apart).

The 30-45-60 formula works on a percentage basis.

30 degrees away is 25%

45 degrees away is 50%

60 degrees away is 75%

A key point to remember is this is talking about DEGREES AWAY.

The next key point to remember is that this is the percentage of the CYL POWER, not the SPH POWER.

So, using the example above

-7.00 -1.00 090 if we wanted to find the power of the lens 45 degrees away from this either at 135 or at 45 degrees we would take 50% of the CYL power. -1.00 times 0.50 = -0.50 diopters. This power is then added to the CYL power to give you the power of the lens 45 degrees away. -7.00 + -0.50 = -7.50 @45 or -7.50 @ 135. Double check to make sure your answer is not below the lowest possible power (-7.00) or above the highest possible power (-8.00). You can also work from the transposed RX to again double check your work. -8.00 +1.00 180, what is the power 45 degrees away or at 135 or 45 degrees? +

Step 1) Take half the CYL power. +1.00 * 0.50 = +0.50

Step 2) Add this power to your sphere power. -8.00 + +0.50 = -7.50 @135 or -7.50 @045

Your answers are both the same regardless if you are working in plus cylinder form or minus cylinder form.

*** Double checking your answers only works this way @045 degrees away.

If you are trying to find the power 30 degrees away, at @060 then you must use 60 degrees away from the transposed RX to arrive at the same point and power of the lens. 60 degrees away from

-8.00 +1.00 180 is at 060 degrees. The power should be the same, let’s try it out.

What is the power of the lens 30 degrees away from this RX from above? (-7.00 -1.00 @090) Power @060

1) 25% of the CYL = -0.25

2) Add power to SPH = -7.00 + -0.25 = -7.25 @060

Double Check (must use 60 degrees away)

1) 75% of the CYL = +0,75

2) Add power to SPH = -8.00 + + 0.75 = -7.25 @060

Practice Problems)

1) What is the power of a lens 30 degrees away if the RX is -12.00 -2.50 127?

2) What is the power of a lens at 080 degrees if the RX is -2.00 -2.00 020?

3) What is the RX of a lens if the power @095 is -3.00, @125 it is -2.00?

4) What is the RX of a lens if the power is -1.00 @130 & PL @085?

Answers)

1) -12.63 @097

2) -3.50 @080

3) -3.00 + 4.00 095 or +1.00 -4.00 005

4) +1.00 -2.00 040 or -1.00 +2.00 130