What is vertex distance and why does it matter for contact lenses?

Vertex distance is the gap between the back surface of a spectacle lens and the front of the cornea, typically 12 to 14 mm. Because spectacle lenses sit away from the eye while contact lenses rest directly on the cornea (vertex distance zero), the same physical lens power produces a different effective correction at the eye plane. For prescriptions stronger than approximately +/- 4.00 dioptres this difference becomes clinically significant, and the contact lens power must be adjusted using the vertex distance formula: F_contact = F_spectacle / (1 - d x F_spectacle), where d is the vertex distance in metres.

Do I need a vertex distance correction for low prescriptions?

For prescriptions below +/- 4.00 dioptres the vertex correction is generally less than 0.25 D, which falls within the standard rounding step used for contact lens powers. Optometrists typically apply vertex correction for prescriptions of +/- 4.00 D or stronger. For lower powers, the spectacle sphere and cylinder values are usually carried across directly to the contact lens prescription. Always confirm with your optometrist, as individual fitting factors also apply.

Is this calculator a substitute for an optometrist fitting?

No. This calculator demonstrates the vertex distance formula used in optical theory and can help you understand how your spectacle prescription relates to a contact lens prescription. Contact lens fitting involves many additional factors including corneal curvature (base curve), lens diameter, tear film, and lens material. A registered optometrist must perform a contact lens fitting and issue a valid contact lens prescription before you purchase or wear contact lenses.

Contact Lens Vertex Distance Calculator

Convert a spectacle lens prescription to equivalent contact lens powers using the vertex distance formula. Contact lenses sit on the cornea (zero vertex distance), so higher-power prescriptions need adjustment from the spectacle values recorded at 12 to 14 mm.

Enter your spectacle Rx for each eye and the vertex distance used when your glasses were dispensed. The calculator applies the standard optical formula to each principal meridian, correcting both the sphere and the cylinder.

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Reviewed June 2026 Standard vertex distance correction formula as used in clinical optometry.

Right Eye (OD)

Sphere (D, e.g. -5.25 or +3.00)

Cylinder (D, e.g. -1.50; 0 if none)

Axis (degrees, 0 to 180)

Left Eye (OS)

Sphere (D, e.g. -5.25 or +3.00)

Cylinder (D, e.g. -1.50; 0 if none)

Axis (degrees, 0 to 180)

Vertex Distance

Vertex distance (spectacle back-vertex to cornea)

Contact Lens Prescription (Vertex-Corrected)

OD Sphere (CL)
-
Right eye contact lens

OD Cylinder (CL)

Right eye cylinder

OS Sphere (CL)
-
Left eye contact lens

OS Cylinder (CL)

Left eye cylinder

Right Eye (OD) Full Working

Spectacle Rx

Sphere-

Cylinder-

Axis-

Vertex Correction

Vertex distance (d)-

d in metres-

Sphere correction-

Cylinder correction-

Contact Lens Rx

OD sphere (CL)-

OD cylinder (CL)-

Axis (unchanged)-

Left Eye (OS) Full Working

Spectacle Rx

Sphere-

Cylinder-

Axis-

Vertex Correction

Vertex distance (d)-

d in metres-

Sphere correction-

Cylinder correction-

Contact Lens Rx

OS sphere (CL)-

OS cylinder (CL)-

Axis (unchanged)-

Note: Enter your spectacle prescription above to see your vertex-corrected contact lens powers.

What is Vertex Distance?

When you wear spectacles, the lenses sit approximately 12 to 14 mm in front of your corneas. This separation is called the vertex distance. Contact lenses, by contrast, rest directly on the corneal surface, giving an effective vertex distance of zero. Because optical power varies with the position of the lens relative to the eye, a spectacle prescription cannot simply be copied across to a contact lens prescription for higher powers.

The difference is negligible for low prescriptions (below about plus or minus 4.00 dioptres) but becomes clinically meaningful for stronger corrections. Ignoring vertex distance in a high myope or hyperope can result in over- or under-correction of several tenths of a dioptre.

The Vertex Distance Formula

The standard formula for converting a spectacle lens power (F_s) to an equivalent contact lens power (F_c) at vertex distance d (in metres) is:

F_c = F_s ÷ (1 − d × F_s)

For a sphere-only prescription the formula is applied directly to the sphere power. When there is a cylinder the correction cannot be applied to the cylinder value on its own, because vertex distance acts on power and the effect is nonlinear. The rigorous clinical method corrects each principal meridian separately - the sphere meridian and the sphere-plus-cylinder meridian - and then rebuilds the contact lens cylinder as the difference between the two corrected meridians. The corrected sphere meridian becomes the contact lens sphere. The axis does not change, because vertex distance affects optical power, not the orientation of astigmatism.

Worked Example (Matches Calculator Defaults)

Using the default inputs: OD sphere -6.00 D, cylinder -1.50 D, axis 90; OS sphere -5.00 D, cylinder -1.00 D, axis 75; vertex distance 13 mm (0.013 m). Each eye is worked meridian by meridian. Meridian 1 is the sphere power, meridian 2 is sphere plus cylinder, and the contact lens cylinder is the difference between the two corrected meridians.

Eye	Component	Spectacle (D)	Formula	Contact Lens (D)
OD	Meridian 1 (sphere)	-6.00	-6.00 / (1 - 0.013 x -6.00)	-5.57
OD	Meridian 2 (sphere + cyl)	-7.50	-7.50 / (1 - 0.013 x -7.50)	-6.83
OD	Cylinder (CL)	-1.50	meridian 2 − meridian 1	-1.27
OD	Axis	90°	Unchanged	90°
OS	Meridian 1 (sphere)	-5.00	-5.00 / (1 - 0.013 x -5.00)	-4.69
OS	Meridian 2 (sphere + cyl)	-6.00	-6.00 / (1 - 0.013 x -6.00)	-5.57
OS	Cylinder (CL)	-1.00	meridian 2 − meridian 1	-0.87
OS	Axis	75°	Unchanged	75°

The contact lens sphere is the corrected sphere meridian: OD -5.57 D and OS -4.69 D. The cylinder is the difference between the two corrected meridians, computed from the unrounded values before display, giving OD -1.27 D and OS -0.87 D. Correcting each meridian separately shifts the cylinder more than correcting the cylinder value on its own would (which would have given OD -1.47 D), because the vertex effect is nonlinear. Results are shown to two decimal places. In practice, contact lens powers are manufactured in steps of 0.25 D, so your optometrist rounds to the nearest available power.

When Does Vertex Distance Matter?

Spectacle Power	Vertex Correction at 13 mm	Clinical Significance
+/- 1.00 to 3.25 D	Less than 0.13 D	Within rounding step; usually ignored
+/- 3.50 to 5.75 D	0.15 to 0.40 D	Borderline; optometrist may apply correction
+/- 6.00 D and above	0.43 D or more	Significant; correction should always be applied

Positive vs Negative Prescriptions

For myopic (negative) prescriptions the contact lens power is less negative than the spectacle power. For hyperopic (positive) prescriptions the contact lens power is less positive. This is because moving a diverging lens closer to the eye reduces the vergence it must supply; moving a converging lens closer to the eye requires less converging power to achieve the same focal point.

Important Disclaimer

This calculator is an educational tool illustrating the vertex distance formula. A contact lens prescription is a regulated medical device prescription in New Zealand. Only a registered optometrist or ophthalmologist can fit contact lenses and issue a valid contact lens prescription. The prescription includes base curve, diameter, and other fitting parameters that this calculator does not address. Do not use these results to purchase or wear contact lenses without a professional fitting.

Related Calculators

Method: Vertex distance correction formula F_c = F_s / (1 - d x F_s). The sphere is corrected directly. For an astigmatic prescription each principal meridian (sphere, and sphere plus cylinder) is corrected separately and the contact lens cylinder is rebuilt as the difference between the two corrected meridians. Axis is unchanged. Standard clinical optometry reference: Tunnacliffe A.H., Introduction to Visual Optics; Bennett A.G. & Rabbetts R.B., Clinical Visual Optics.

This calculator is for educational and illustrative purposes only. It does not constitute a contact lens prescription. Always obtain a professional contact lens fitting from a registered optometrist or ophthalmologist before purchasing or wearing contact lenses.