The spherical equivalent and cylinder transposition calculator gives the spherical equivalent, the transposed prescription and the power vectors of a glasses prescription from the sphere, cylinder and axis.
How the calculation works
- Enter the sphere, the cylinder and the axis.
- Read the spherical equivalent.
- Use the transposed form and the power vectors as needed.
Example
A prescription of −2.50 −1.25 × 90 has a spherical equivalent of −2.50 + (−1.25 / 2) = -3.125 D. Transposed it is -3.75 +1.25 × 180. The power vectors are M = -3.125 D, J0 = -0.625 D and J45 = 0.000 D.
Why it matters
The calculator helps optometry students, opticians, ophthalmologists and researchers who convert prescriptions between forms or who need the equivalent sphere of a refractive error.
Good to know
The spherical equivalent is an approximation: two eyes with the same equivalent but different cylinders do not see equally well, because the cylinder remains uncorrected when only the equivalent sphere is used. It is useful for statistics, for contact lens estimates and for planning, but a full prescription needs the sphere, cylinder and axis. The convention for the axis uses the standard of the TABO scheme from 1 to 180 degrees, with 90 degrees at the vertical. The transposition does not change the optical effect, but some lens catalogs or contact lenses are only made in certain cylinder forms, so the plus or minus form matters when ordering. Always check the prescription written by the practitioner. The same prescription can be written in either form, and the choice usually follows the habit of the practice or the requirements of the lens laboratory.
Related tools
The keratometry calculator treats corneal power, the vertex distance calculator converts lens power for contact lenses, the reading glasses calculator treats near correction and the visual acuity calculator converts acuity notations.