Lens Power & Vertex Distance Calculator (Glasses to Contacts)
Convert a glasses prescription to contact-lens power (or back) with vertex-distance compensation for sphere, cylinder and axis, one or both eyes, with contact-lens rounding, spherical equivalent, a vertex table and diopter ↔ focal-length conversion.
How it works
Compensated power F′ = F ÷ (1 − d × F), with d = (old vertex distance − new vertex distance) in metres (positive when the lens moves toward the eye), applied to each principal meridian (sphere, and sphere + cylinder) · cylinder = difference of the compensated meridians, axis unchanged · spherical equivalent = sphere + cylinder ÷ 2 · D = 1 ÷ focal length (m)
A lens works by changing the vergence of light, and that vergence keeps changing as the light travels, so the same eye needs a different power when the lens sits in a frame 12 mm away than when it sits on the cornea. Minus (myopic) lenses must be weaker the closer they get, and plus lenses stronger; the change grows roughly with the square of the power, so it is negligible below ±4 D, about half a diopter at −8 D and several diopters for very high plus corrections. For astigmatism the calculator compensates the two principal meridians separately — the sphere and the sphere plus cylinder — and rebuilds the prescription from them, which slightly reduces a minus cylinder; the axis does not change. You can convert glasses to contacts, contacts back to glasses, or one frame position to another, for one or both eyes, write the cylinder in minus or plus form, and round to the steps soft lenses are actually made in. The table and chart show the power needed at a range of vertex distances, and the focal-length mode converts diopters to focal length and back.
Worked example
Glasses −7.50 / −1.50 × 180 at 12 mm: the 180° meridian is −7.50 ÷ (1 + 0.012 × 7.50) = −7.50 ÷ 1.09 = −6.88 D and the 90° meridian (−9.00 D) becomes −9.00 ÷ 1.108 = −8.12 D. The cylinder is −8.12 − (−6.88) = −1.24 D, so the contact-lens power is about −7.00 / −1.25 × 180, with a spherical equivalent of −7.50 D. Going the other way, a −8.00 D contact lens needs about −8.75 D in glasses at 12 mm.
Sources: Omni Calculator — Contact lens vertex calculator (toric worked example) · FTC — Contact Lens Rule (prescription requirements)
Frequently asked questions
Why do my contacts have a lower number than my glasses?
Vertex compensation — a minus lens loses effective power as it moves closer to the eye, so the contact lens needs less minus to give the same correction. For plus prescriptions it is the other way round: the contact lens is stronger.
How is astigmatism (cylinder) converted?
Each principal meridian is converted on its own: the sphere, and the sphere plus the cylinder. The new cylinder is the difference between the two converted meridians, so a minus cylinder usually gets slightly smaller. The axis stays the same.
When do I need a toric contact lens?
As a rule of thumb, 0.75 D of cylinder or more is corrected with a toric lens. Smaller amounts are often handled with a spherical lens at the spherical equivalent (sphere plus half the cylinder), which the calculator shows.
Does this apply to reading glasses?
Only above about +4 D; typical readers of +1 to +3 change by less than 0.25 D, within the prescribing step.
Can I buy contact lenses with my glasses prescription?
No. A contact-lens prescription also needs a base curve, diameter and brand chosen at a fitting, and in many countries (including the US) contacts can only be sold against a contact-lens prescription.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.