Three steps, in this order
- Add the cylinder to the sphere. New SPH = SPH + CYL.
- Change the sign of the cylinder. New CYL = −CYL. The number stays the same.
- Turn the axis through 90°. An axis up to 90 gains 90; an axis above 90 loses 90, so the new axis always lies between 1 and 180.
The converter prints these three steps under the result, so the working can be checked or copied onto the job card. Run the same three rules on a minus-cylinder prescription and you get plus cylinder back. If a prescription's layout is unfamiliar, the guide on how to read an eye prescription shows where the sphere, cylinder and axis are written.
Worked example: a plus-cylinder prescription for the lab
An ophthalmologist writes the right eye as +1.50 +2.00 × 75. The lab surfaces in minus cylinder.
| Step | The converter shows |
|---|---|
| 1 | Step 1: New SPH = (+1.50) + (+2.00) = +3.50 D |
| 2 | Step 2: Change Sign = -2.00 D |
| 3 | Step 3: Rotate Axis = 75° + 90° = 165° |
| Result | +3.50 -2.00 x 165° |
Two more from the converter: −1.00 +1.50 × 180 becomes +0.50 -1.50 x 90°, and a minus-cylinder reading of −2.00 −1.00 × 90 becomes -3.00 +1.00 x 180°.
Writing it on a lab order
- Say which form you are sending. Most surfacing labs and stock single-vision ranges work in minus cylinder.
- Write the axis with three digits (075, 090, 165) so a handwritten 7 is not read as 1. Write 180, never 0.
- Keep every sign, including on a plano or +0.00 sphere, and convert both eyes the same way.
- For a full two-eye prescription with the spherical equivalent alongside, use the transposition calculator.
Checking a lensmeter reading
A manual lensmeter gives one form or the other depending on which line you focus first. A reading of −2.00 −1.50 × 30 and a reading of −3.50 +1.50 × 120 are the same lens. Converting one to the other confirms that a finished pair matches the order.
Limits. The converter works on one eye at a time and does not check the axis: enter a whole number from 1 to 180. With a cylinder of 0.00 the lens is a sphere and the axis in the result has no meaning. See the medical disclaimer.
Questions
Does transposing a prescription change the lens?
No. Both forms describe the same two principal powers at the same two meridians. A lens made to either form is the same lens.
Why do labs ask for minus cylinder?
Nearly all modern spectacle lenses carry the toric surface on the inside, facing the eye, and a back-surface toric is described in minus cylinder. Stock single-vision lenses are listed the same way, so sending minus cylinder saves the lab a conversion.