Cylinder transposition calculator

Convert a refraction between plus-cylinder and minus-cylinder notation. Enter sphere, cylinder and axis and the transposed equivalent is returned.

How transposition works

To transpose, add the cylinder to the sphere, reverse the sign of the cylinder, and rotate the axis by 90 degrees (adding 90 if the axis is 90 or less, subtracting 90 if it is greater than 90). The two notations describe the same lens.

Frequently asked questions

How do you transpose plus cylinder to minus cylinder?

Add the cylinder power to the sphere, change the sign of the cylinder from plus to minus, and rotate the axis by 90 degrees. For example, +2.00 +1.00 x 090 becomes +3.00 -1.00 x 180.

Does transposition change the prescription?

No. Plus-cylinder and minus-cylinder notation describe the identical optical correction; only the way it is written changes.

See also the toric IOL rotation calculator.