Contact Lens Vertex Calculator

Find out what power contact lens will fit you using this contact lens vertex calculator!

Power after moving 12 mm closer to the eye-7.2993 dioptresF ÷ (1 − dF) — this is why a contact lens prescription differs from spectacles, and the correction grows with the power

Image distance121.9512 mm121.951 mm in front of the lens — a virtual image, visible only by looking through

Magnification0.02439×virtual, upright, and reduced to 0.024×

Image height487.8049 µm0.488 mm, upright

Focal length-125 mmdiverging

Optical power-8 dioptresthe reciprocal of the focal length in metres — how spectacle prescriptions are written

Object distance in focal lengths40fa diverging element always gives a virtual, upright, reduced image wherever the object sits

Focal length from the surfaces115.3846 mm(n−1)(1/R₁ − 1/R₂) with n = 1.52 and a flat second face

Power from the surfaces8.6667 dioptres

Change in power0.7007 dioptressignificant — strong prescriptions must be converted

The formula

1/f = 1/d_o + 1/d_i; m = −d_i ÷ d_o; D = 1 ÷ f

Signs carry the physics

The thin-lens equation is simple arithmetic; the conventions are where errors live. A positive image distance means a real image, formed behind the lens, which you could catch on a screen. A negative one means a virtual image on the same side as the object, visible only by looking through the lens. A negative magnification means inverted.

Where the object sits relative to the focal length determines the character of the image entirely. Beyond 2f you get the reduced inverted image a camera uses. Between f and 2f you get a magnified inverted one, which is a projector. Inside f the image turns virtual, upright and magnified — a magnifying glass. Exactly at f the rays emerge parallel and the image goes to infinity, which is what a collimator exploits.

Dioptres are simply the reciprocal of focal length in metres, and they add: two thin lenses in contact have the sum of their powers. That additivity is why prescriptions are written this way rather than in millimetres of focal length.

Vertex distance is a real clinical correction. Moving a lens closer to the eye changes its effective power, and the shift grows with the prescription — negligible below about 4 dioptres, and several tenths of a dioptre for strong corrections, which is why contact lens and spectacle prescriptions genuinely differ.