A cylindrical lens used to correct for astigmatism may be defined either with a positive or negative cylinder. A prescription can be transformed into the other kind of lens using a number of simple rules.


Format for a cylindrical lens prescription: <spherical lens> <cylinder> x <axis>


A positive (+) spherical lens indicates a plus (convex) lens for a patient with hyperopia.

A negative (-) spherical lens indicates a minus (concave) lens used for a patient with myopia.

A positive (+) cylinder indicates a plus (convex) cylinder for a patient with astigmatism.

A negative (-) cylinder indicates a minus (concave) cylinder for a patient with astigmatism.


Transformation for the prescription S1 C1 x A1


New prescription S2 C2 x A2


S2 = S1 + C1


C2 = (-1) * (C1)


A2 = either (A1 + 90 degrees) or (A1 - 90 degrees), whichever gives a positive number less than 180°

Converted Parameter

New Values


(original sphere) + (original cylinder)


(-1) * (original cylinder)


(degrees) + 90 (if positive number and < 180) OR

(degrees) - 90 (if positive number and < 180)



• An original degrees of 90 could convert to 0 or 180.


To read more or access our algorithms and calculators, please log in or register.