This article is from the Vision and Eye Care FAQ, by grants@research.canon.com.au (Grant Sayer) with numerous contributions by others.
To convert from "plus-cyl" form to "minus-cyl" form use the following steps:
1. Add the cylinder power to the sphere
2. Change the sign of the cylinder from + to -
3. Add 90 degrees to the axis if the original axis is less than 90, or
4. Subtract 90 degrees from the axis if the original is greater than 90.
To convert from "minus-cyl" to "plus-cyl" form the steps are reversed, i.e
1. Add the cylinder power to the sphere power
2. Change the sign of the cylinder from - to +
3. Add 90 degrees to the axis of the cylinder if axis < 90
4. Subtract 90 degress from the axis if axis > 90
Other WWW references:
URL: http://www.west.net/~eyecare/optical_lens_prescriptions.html
 
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