Prescription transposition.

The short answer

To transpose a prescription: add the cylinder to the sphere, change the sign of the cylinder, and move the axis by 90 degrees. Example: -2.25 -1.50 x 180 becomes -3.75 +1.50 x 090.

Worked example

Take -2.25 -1.50 x 180 (minus cylinder). New sphere = -2.25 + (-1.50) = -3.75. New cylinder = +1.50. Axis 180 is above 90, so subtract 90: 090. Result: -3.75 +1.50 x 090. The calculator prints exactly this, and the same steps run backwards give the original.

Second case, plus to minus: -1.00 +0.25 x 180 becomes -0.75 -0.25 x 090 (sphere -1.00 + 0.25 = -0.75, cylinder -0.25, axis 180 - 90 = 90).

How it works

New sphere = sphere + cylinder. New cylinder = -cylinder. New axis = axis + 90 if the axis is 90 or less, otherwise axis - 90 (so the axis stays between 1 and 180). Both forms describe the same lens: the steepest and flattest meridians are simply described from the other end.

Which notation is used varies. Wikipedia notes that in the US optometrists commonly write minus cylinder while ophthalmologists often write plus cylinder. Check with your lab or eye-care provider which one a form wants.

Limits. This changes how a prescription is written, not what it is. It does not handle prism, add power or contact lens parameters, and it does not check whether a prescription is valid. Order lenses from the prescription as issued.

Sources (opened 2026-10-08): Wikipedia, Eyeglass prescription; American Academy of Ophthalmology, How to Read an Eyeglasses Prescription.

FAQ

How do I convert plus cylinder to minus cylinder?

Add the cylinder to the sphere to get the new sphere, flip the sign of the cylinder, and rotate the axis by 90 degrees (add 90, or subtract 90 if the axis is above 90). For example, -1.00 +0.25 x 180 becomes -0.75 -0.25 x 090.

Is a transposed prescription a different prescription?

No. Plus and minus cylinder notation describe the identical lens. Only the way the powers are written changes.

What happens to the axis when I transpose?

It moves by 90 degrees and stays between 1 and 180. Axis 180 becomes 90, axis 90 becomes 180, and axis 45 becomes 135.

Which notation should I use to order glasses?

Use the one that is on your prescription, or ask your optician which their system takes. Transposing is only a notation change, so both forms describe the same lens.

Does this work with a zero cylinder?

If there is no cylinder there is nothing to transpose, and the sphere stays as it is.

Can I use this to change my own prescription?

No. It only rewrites a prescription you already have. Only an eye-care professional can prescribe or change one.

Need the single-number summary of the same prescription? Try the spherical equivalent calculator.