Lens transposition calculator
Lens transposition rewrites a spectacle prescription from minus-cylinder to plus-cylinder form, or back, without changing the lens. Add the cylinder to the sphere, change the sign of the cylinder, and turn the axis by 90 degrees: add 90 if the axis is 90 or less, subtract 90 if it is more.
Type one eye below. It works both ways, minus to plus and plus to minus, and accepts the same values a prescription allows: sphere up to ±20.00 and cylinder up to ±10.00 in 0.25 steps, axis 0 to 180.
Transposed
-2.75 / +0.75 × 90
The same lens as the one you typed, written in plus-cylinder form.
The three rules
- New sphere = sphere + cylinder. −2.00 and −0.75 make −2.75.
- New cylinder = same number, opposite sign. −0.75 becomes +0.75.
- New axis = axis ± 90. Add 90 when the axis is 90 or less, subtract 90 when it is more, so the answer stays between 1 and 180. 180 becomes 90.
Worked examples
| Written as | Transposed |
|---|---|
| -2.00 / -0.75 × 180 | -2.75 / +0.75 × 90 |
| +1.50 / +1.00 × 45 | +2.50 / -1.00 × 135 |
| -1.25 / -0.75 × 170 | -2.00 / +0.75 × 80 |
| +0.75 / -0.75 × 20 | +0.00 / +0.75 × 110 |
The last row ends with a sphere of +0.00. Some prescriptions write that as plano.
Why opticians transpose
The same eye can reach the counter written two ways. One doctor writes plus cylinder, another writes minus, and a lab or a lens supplier quotes and stocks lenses in one form only. Transposing lets you send the lab the form it works in, pick the right power from your own stock, and compare last year's prescription with this year's when they were written differently. Mistakes happen when it is done in your head at the counter and again on the job card. A sign gets flipped twice, or the axis is turned the wrong way.
Check your answer
Two quick checks catch almost every slip. First, the spherical equivalent (sphere plus half the cylinder) is the same in both forms. Second, transposing the answer again gives back what you started with. If either check fails, look at the sign of the cylinder first.
Transposing inside LensVerge
In LensVerge the prescription form has a Transpose button for each eye that does this same calculation. Values are checked as they are typed: quarter steps, and an axis whenever there is a cylinder. The prescription then travels with the sale onto the job card the lab works from. Read how to read an eyeglass prescription for SPH, CYL, AXIS, ADD and PD in plain words, or see the optical POS for how a prescription is attached to a bill. Another free tool: spectacle GST calculator.