Change a spectacle prescription between plus and minus cylinder form, and see its spherical equivalent and the power in each principal meridian. For opticians, optometrists and anyone comparing two prescriptions.
Worked examples
−2.00 −1.00 × 30: sphere −2.00 + (−1.00) = −3.00, cylinder becomes +1.00, axis 30 + 90 = 120, so it's −3.00 +1.00 × 120. Spherical equivalent −2.50 D; −2.00 D along 30° and −3.00 D along 120°.
+1.00 −3.00 × 45 (mixed astigmatism: one meridian plus, one minus): +1.00 + (−3.00) = −2.00, so it's −2.00 +3.00 × 135.
To combine two prescriptions whose axes differ, use the crossed cylinders calculator; for contact lens power, the vertex distance calculator.
Checked on 19 October 2026. For eye-care professionals; a prescription should come from an eye examination.
Frequently asked questions
How do you transpose a prescription?
Three steps: add the cylinder to the sphere to get the new sphere; change the sign of the cylinder; and turn the axis by 90° (add 90 if the axis is 90 or less, take 90 away if it's more). The lens itself doesn't change: both forms describe the same powers in the same meridians.
Why are there two forms?
Ophthalmologists have traditionally written prescriptions in plus cylinder and optometrists and opticians in minus cylinder, and lens labs usually work in minus cylinder. Transposing lets you compare two prescriptions, or order a lens, in the form you need.
What is the spherical equivalent?
The sphere plus half the cylinder: the single spherical power that puts the circle of least confusion on the retina. It's the same in both forms, and it's often used to choose a spherical contact lens or to compare two refractions.
What is the power cross?
The power along each of the lens's two principal meridians, 90° apart: the sphere acts along the axis meridian, and sphere plus cylinder along the meridian at right angles. Transposition never changes it.
