Vision Prescription Converter

Glasses sit about 12 mm in front of the eye and a contact lens sits on it. Moving a lens closer changes what it does, so the same eye needs a slightly different power in each. This converts a glasses prescription into the contact lens power it implies.

The vertex formula:

Contact lens power = P ÷ (1 − d × P)
where P is the glasses power in dioptres and d is the vertex distance in metres (typically 0.012 m = 12 mm)

A minus lens loses strength as it moves closer, and a plus lens gains it. The shift grows with the square of the power, so it barely matters for mild prescriptions and matters a lot for strong ones. Most practitioners start allowing for it at about ±4.00 D, though the rounding to 0.25 D steps can already move a ±3.50 by one step.

With astigmatism, each of the two main meridians is converted on its own: the sphere, and the sphere plus the cylinder. The new cylinder is the difference between them, which is why a strong cylinder can shrink a little in a contact lens.

Spherical Equivalent (SE) = Sphere + (Cylinder ÷ 2)

People with little astigmatism, about 0.75 D or less, are usually fitted with an ordinary spherical soft lens, and its power starts from the spherical equivalent, vertex-adjusted. More astigmatism than that needs a toric lens with its own axis.

What each prescription term means:

• Sphere (SPH): the primary correction strength in diopters. Negative = nearsighted (myopia); positive = farsighted (hyperopia). Range: typically −20.00 to +20.00 D.
• Cylinder (CYL): astigmatism correction strength. Negative in minus-cylinder notation, which most optometrists use; positive in plus-cylinder notation, which many ophthalmologists use. Convert a plus-cylinder prescription to minus first with the glasses prescription converter.
• Axis: the angle of the cylinder correction, in degrees from 1 to 180. Only meaningful when CYL is present.
• Add: additional magnification for reading (presbyopia). Typically +0.75 to +3.50 D. Present on bifocal or progressive prescriptions.
• Prism: corrects eye alignment issues (measured in prism diopters). Not always present.

Worked example:

Right eye: −6.00 SPH, −1.00 CYL, Axis 175
Sphere meridian: −6.00 ÷ (1 + 0.012 × 6.00) = −5.60, which rounds to −5.50
Cylinder meridian: −7.00 ÷ (1 + 0.012 × 7.00) = −6.46, so the cylinder is −6.46 − (−5.60) = −0.86, which rounds to −0.75
Contact lens: −5.50 / −0.75. The axis carries across, though a toric lens is checked on the eye at the fitting.

Prescription strength reference:

• Mild: ±0.50 to ±2.00 D | Moderate: ±2.25 to ±5.00 D | Strong: ±5.25 to ±9.00 D | Very strong: > ±9.00 D