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Rx transposition

To transpose a prescription: add the sphere and cylinder for the new sphere, flip the sign of the cylinder, and rotate the axis 90 degrees while keeping it on the 1 to 180 scale. The canonical example: -2.00 -1.50 x 180 transposes to -3.50 +1.50 x 090. Both forms describe exactly the same lens.

Transposition calculator

Enter each eye in either minus-cylinder or plus-cylinder form. The calculator returns the other form with the steps written out.

OD (right eye)
OS (left eye)

OD result

-2.00 -1.50 x 180 transposes to -3.50 +1.50 x 090

  1. New sphere = sphere + cylinder = -2.00 + -1.50 = -3.50.
  2. New cylinder = cylinder with the sign flipped: -1.50 becomes +1.50.
  3. New axis = axis rotated 90 degrees, kept between 1 and 180: 180 becomes 090.

Both notations describe the same lens; the power in every meridian is unchanged.

OS result

-1.75 -0.75 x 005 transposes to -2.50 +0.75 x 095

  1. New sphere = sphere + cylinder = -1.75 + -0.75 = -2.50.
  2. New cylinder = cylinder with the sign flipped: -0.75 becomes +0.75.
  3. New axis = axis rotated 90 degrees, kept between 1 and 180: 005 becomes 095.

Both notations describe the same lens; the power in every meridian is unchanged.

Practice transposition

Unlimited generated problems with exact answers and worked steps.

Go deeper

The step-by-step transposition guide covers the axis wrap, plano and sphere-only edge cases, and how to self-check with the meridian power tool.

Frequently asked questions

How do you transpose a prescription?

Three steps: add the sphere and cylinder to get the new sphere, flip the sign of the cylinder, and rotate the axis 90 degrees while keeping it between 1 and 180. For example -2.00 -1.50 x 180 becomes -3.50 +1.50 x 090.

Why do prescriptions come in minus-cylinder and plus-cylinder forms?

They describe the same lens two ways. Optometrists commonly write minus cylinder and ophthalmologists plus cylinder; labs typically surface lenses in minus cylinder. Transposition converts between the two without changing the optics.

What happens to the axis when it passes 180?

Subtract 180 so it stays on the 1 to 180 scale. Axis 120 becomes 30 after adding 90. By convention the horizontal meridian is written 180, never 0.

Does transposing change the power of the lens?

No. The power in every meridian is identical in both forms - only the notation changes. You can verify this with the meridian power tool.