Polyatic Cylinder Transposition Calculator
All tools

Cylinder transposition calculator

Rewrite a glasses prescription from plus to minus cylinder, or back, with each step shown.

Arithmetic on a prescription you already have. It is not an eye test, not a prescription and not advice on buying lenses.

Privacy: your prescription stays on this device. The arithmetic runs inside this page; nothing you type is sent or stored. The page sends an anonymous page-view count and two fixed event names (cyl-transpose, cyl-copy), never a number you typed.

How to use it

  1. Type one line per eye the way it is written: -2.00 / +1.50 x 090, -2.00 +1.50 x 90, +1.25 DS, plano / -0.75 x 180 or pl -0.75 x180. Start a line with R, L, OD or OS if you like; unlabelled lines are read right eye first, as prescriptions are written.
  2. Or switch to SPH / CYL / AXIS boxes and fill in the columns of the form.
  3. Read each eye in the other form and the three numbered steps worked in its own numbers. Plus cylinder becomes minus cylinder and minus becomes plus.
  4. Tap Copy result for plain text with both eyes, both forms and the steps, ready to paste into notes or a lab order.

How a prescription line is written

A line reads sphere, cylinder, axis: in -2.00 +1.50 x 090 the sphere is -2.00 dioptres, the cylinder +1.50 dioptres, and the cylinder's axis is 90 degrees. The two powers are always signed and written to two decimals, and lenses are graded in steps of 0.25 dioptres, so a power such as -2.10 is almost always a typing slip. The axis is a whole number from 1 to 180: 90 is vertical, and 180 is horizontal. Axis 0 is the same line as 180, and prescriptions write 180. DS (dioptres sphere) after a single power, as in +1.25 DS, says there is no cylinder on purpose. Plano or PL means a power of zero. OD is the right eye and OS the left; UK forms often write RE and LE. ADD is the extra plus power for reading and is not changed by transposing; nor is prism, which is measured in prism dioptres with a base direction such as BI or BU.

Plus and minus cylinder are two ways of writing the same lens. With a cylinder, a lens has two main powers 90 degrees apart. Minus cylinder form starts from the more plus of the two, plus cylinder form from the more minus. -2.25 -1.50 x 180 and -3.75 +1.50 x 090 both describe a lens of -2.25 along the horizontal and -3.75 along the vertical. Optometrists and lens labs mostly use minus cylinder, and some ophthalmologists write plus cylinder, so a plus-cylinder prescription is often transposed before the lenses are made.

What it cannot do

  • It does not test eyes or write prescriptions. A prescription comes from an eye examination: in the UK, the NHS says the optometrist who tests your eyes must give you your prescription afterwards.
  • It does not convert to or from contact-lens powers, and it does not adjust for vertex distance (the gap between the lens and the eye that matters above about ±4.00).
  • It gives no spherical equivalent.
  • It does not check that a prescription is right. It only rewrites the line typed, in the other form, and flags typing that looks wrong.
  • One line per eye, two lines at most. Prism and ADD are carried over as typed, never converted.

Question

How do you convert plus cylinder to minus cylinder?

Three steps. 1. Add the cylinder to the sphere; the sum is the new sphere. 2. Change the sign of the cylinder. 3. Turn the axis by 90 degrees: add 90 if the axis is 90 or less, subtract 90 if it is more, so it stays between 1 and 180.

Worked example, -3.00 +2.00 x 030: (-3.00) + (+2.00) = -1.00; +2.00 becomes -2.00; 030 + 90 = 120. The minus-cylinder form is -1.00 -2.00 x 120. The same steps take a minus-cylinder line back to plus: (-1.00) + (-2.00) = -3.00, -2.00 becomes +2.00, 120 - 90 = 030. Transposing twice always gives back the line you started with, which is a handy check on hand working.

Sources

Made with AI tools.