Calculate lens power in diopters, convert prescriptions between forms, compute focal lengths, and estimate contact lens power from spectacle Rx.
The diopter (D) is the unit of measurement for the optical power of a lens, defined as the reciprocal of the focal length in meters: 1 D = 1/f. A lens with a power of +2 D focuses parallel light at 0.5 meters, while a -3 D lens diverges light as if it came from a virtual focus at 0.33 meters behind the lens. Diopters are the standard unit used in eye care prescriptions worldwide.
An eyeglass prescription typically includes three values: sphere (overall power), cylinder (astigmatism correction), and axis (orientation of astigmatism). Understanding these values helps patients make informed decisions about their corrective lenses. The spherical equivalent—calculated as sphere plus half the cylinder—gives a single number that represents the average refractive error.
This calculator performs comprehensive prescription analysis: compute spherical equivalents, convert between plus and minus cylinder forms, estimate contact lens power with vertex distance correction, calculate focal lengths, and determine near-vision prescriptions with reading additions. It also includes reference tables for common diopter values and their applications.
Use this calculator when you want to interpret lens power, spherical equivalent, focal length, or prescription transposition without doing the notation changes by hand.
It is useful for understanding lens math and comparing prescription formats, but it should not replace an eye exam, a fitting, or clinician guidance for new or changing vision problems.
Spherical equivalent: SE = Sphere + Cylinder/2 Focal length: f = 1000/D (mm) = 1/D (m) Vertex correction: D_contact = D_spectacle / (1 − d × D_spectacle) Transpose: Sph' = Sph + Cyl, Cyl' = −Cyl, Axis' = Axis ± 90° Prentice's rule: Prism = D × d (decentration in cm)
Result: SE = -2.25 D, focal length = -500 mm, transposed: -2.50/+0.50×90
A prescription of -2.00/-0.50×180 has a spherical equivalent of -2.25 D (mild myopia), a focal length of 500 mm, and transposes to -2.50/+0.50×90 in plus cylinder form.
Diopter math is most useful for understanding how lens power is expressed and how different prescription formats relate to each other. It can help you read a prescription, estimate focal length, or see why a contact-lens power may not exactly match the spectacle value.
The biggest mistakes are mixing plus and minus cylinder notation, misreading the axis, and treating spherical equivalent as a substitute for a full prescription. Vertex-distance corrections also matter more as lens power increases, so high prescriptions should be interpreted with more care than low ones. Prescription math is helpful, but it does not replace refraction, fitting, and clinical judgment.
Negative diopters indicate a diverging (concave) lens used to correct myopia (nearsightedness). The eye focuses light in front of the retina, and the negative lens moves the focus back onto the retina.
The spherical equivalent (SE = sphere + cylinder/2) represents the average refractive power of an astigmatic prescription as a single sphere value. It's used to estimate overall refractive error and for contact lens fitting.
Glasses sit about 12 mm from the eye (vertex distance), while contacts sit on the cornea. The effective power changes with distance. For prescriptions over ±4 D, vertex correction is clinically significant.
The same astigmatism can be written two ways. Ophthalmologists often use plus cylinder; optometrists use minus cylinder. Transposing: add sphere and cylinder, negate the cylinder, and rotate the axis 90°.
Most people benefit from correction at ±0.50 D or more. Below ±0.25 D is considered clinically insignificant. Prescriptions over ±6 D are considered high and may require special lens designs.
The add power compensates for presbyopia (age-related loss of near focusing). It typically starts at +0.75 to +1.00 D around age 40 and increases to +2.50 to +3.00 D by age 65.