Vertex Distance Calculator: Convert Glasses to Contact Lens Power

Use this vertex distance calculator to convert a lens power from one vertex distance to another, most often from a glasses prescription at 12 mm to a contact-lens starting power at 0 mm. Enter the original and new vertex distances and the lens power, and the calculator returns the exact compensated power, the power rounded to 0.25 D (or 0.125 D or 0.01 D), the power change and how far the lens moved.

How to Use the Vertex Distance Calculator

Enter the original vertex distance (where the power was measured or specified) and the new vertex distance (where the lens will sit), or tap a quick preset: glasses → contacts (12 → 0 mm), contacts → glasses (0 → 12 mm), 13.5 → 12 mm or 12 → 14 mm. Distances can be 0–100 mm.

Basic Mode (Sphere)

Enter a single spherical power in diopters, with a minus sign for minus lenses, and choose the rounding increment. The results show the compensated power rounded to your chosen step, the exact compensated power to three decimals, the original power, the power change and the lens movement (for example, “12 mm closer”).

Advanced Prescription Mode

Enter sphere, cylinder and axis for the right eye (OD) and left eye (OS). Minus-cylinder and plus-cylinder notation both work. For each eye the calculator shows the original prescription, the exact compensated prescription and the rounded prescription, plus the compensated power of each principal meridian.

What Is Vertex Distance?

Vertex distance is the distance between the back surface of a corrective lens and the front of the cornea. A spectacle lens sits a short distance in front of the eye, while a contact lens sits on the cornea. Because the lens position changes its effective power at the eye, a glasses prescription and an equivalent contact-lens power are not always the same number.

Back Vertex Distance (BVD)

Back vertex distance (BVD) is the same measurement taken from the back surface of the spectacle lens to the corneal apex. It depends on the frame, how the lens sits and the wearer’s face, so a measured BVD is more accurate than an assumed value.

Why Is 12 mm Commonly Used?

12 mm is widely used as a reference spectacle vertex distance when no measured BVD is available, and a contact lens is treated as sitting at 0 mm. It is a convention, not the actual distance for every pair of glasses. If the measured BVD is, for example, 10 mm, enter 10 mm as the original vertex distance.

Why Does Vertex Distance Change Lens Power?

A lens brings light to a focus at a set distance behind it. Moving the lens closer to or farther from the eye moves that focal point relative to the eye, so a different power is needed at the new position to give the same correction. The effect grows with lens power and with the size of the move:

• Moving a lens closer to the eye (e.g. glasses to contacts): minus powers become less minus and plus powers become more plus.
• Moving a lens farther from the eye: minus powers become more minus and plus powers become less plus.

What Is the 4-Diopter Rule?

Vertex compensation is often said to matter from about ±4.00 D. At 12 mm, a −4.00 D lens compensates to −3.82 D, which rounds to −3.75 D, so it is roughly where the change reaches a 0.25 D step. Treat it as a rule of thumb, not a cutoff: the effect depends on the power, the distance moved and, for astigmatism, the power of the stronger meridian.

Vertex Distance Formula

Fc = Fs ÷ (1 − d × Fs)

Where:

• Fc = compensated power at the new lens position (D)
• Fs = original lens power (D)
• d = original vertex distance − new vertex distance, in metres (positive when the lens moves closer to the eye, negative when it moves away)

Converting Millimetres to Metres

The formula needs metres: divide millimetres by 1,000. A 12 mm move is d = 0.012 m. Entering 12 instead of 0.012 gives a meaningless result.

Vertex Distance vs Change in Vertex Distance

The formula uses the change in position, not the new distance. From 12 mm to 0 mm the lens moves 12 mm, so d = 0.012. From 13.5 mm to 12 mm it moves 1.5 mm closer, so d = 0.0015. From 12 mm to 14 mm it moves 2 mm away, so d = −0.002.

Glasses to Contact Lens Conversion

For a standard conversion, use an original vertex of 12 mm (or the measured BVD) and a new vertex of 0 mm.

Minus Lens Example: −6.00 D

Fc = −6.00 ÷ (1 − 0.012 × −6.00) = −6.00 ÷ 1.072 = −5.597 D

Rounded to the nearest 0.25 D, the contact-lens starting power is −5.50 D. The minus power became less minus because the lens moved closer to the eye.

Plus Lens Example: +6.00 D

Fc = +6.00 ÷ (1 − 0.012 × +6.00) = +6.00 ÷ 0.928 = +6.466 D

Rounded to the nearest 0.25 D, this is +6.50 D. Plus powers move in the opposite direction and become more plus at the cornea.

Contacts to Glasses: 0 → 12 mm

Going the other way, d = 0 − 0.012 = −0.012. A −5.60 D contact-lens power gives Fc = −5.60 ÷ (1 − (−0.012) × −5.60) = −5.60 ÷ 0.9328 = −6.003 D, about −6.00 D at the spectacle plane.

Vertex Distance Conversion Chart (12 mm to 0 mm)

Spherical spectacle powers at a 12 mm vertex converted to the corneal plane (0 mm):

Spectacle power	Compensated power	Rounded to 0.25 D
−4.00 D	−3.82 D	−3.75 D
−5.00 D	−4.72 D	−4.75 D
−6.00 D	−5.60 D	−5.50 D
−7.00 D	−6.46 D	−6.50 D
−8.00 D	−7.30 D	−7.25 D
+4.00 D	+4.20 D	+4.25 D
+5.00 D	+5.32 D	+5.25 D
+6.00 D	+6.47 D	+6.50 D
+7.00 D	+7.64 D	+7.75 D
+8.00 D	+8.85 D	+8.75 D

A different measured vertex distance gives different values, so use the calculator with your actual BVD where possible.

Vertex Compensation for Astigmatism (Cylinder)

A sphero-cylinder prescription has two principal meridians with different powers, so applying the formula to the sphere alone is not enough. Advanced Prescription mode uses the principal-meridian method.

Principal Meridian Method

Example: −5.00 / −2.00 × 180, converted from 12 mm to 0 mm.

1. Find the two meridians: M1 = sphere = −5.00 D; M2 = sphere + cylinder = −5.00 + (−2.00) = −7.00 D.
2. Compensate each meridian: M1 → −5.00 ÷ 1.060 = −4.717 D; M2 → −7.00 ÷ 1.084 = −6.458 D.
3. Rebuild the prescription: sphere = −4.717 D; cylinder = −6.458 − (−4.717) = −1.741 D; axis stays 180.

Rounded to 0.25 D, the compensated prescription is −4.75 / −1.75 × 180. The cylinder also becomes smaller in magnitude, which is why compensating only the sphere would be inaccurate.

Does the Cylinder Axis Change?

No. The axis describes the orientation of the cylinder, and moving the lens along the line of sight does not rotate it. Only the meridian powers change, so the axis is carried over unchanged.

Frame Changes and Phoropter-to-Frame Compensation

Vertex compensation is not limited to contact lenses. It also applies when a spectacle lens sits at a different distance from the one used during the eye test.

Lens Moved Farther: 12 → 14 mm

d = 12 − 14 = −2 mm = −0.002 m. For −6.00 D: Fc = −6.00 ÷ (1 − (−0.002) × −6.00) = −6.00 ÷ 0.988 = −6.073 D. Moving a minus lens away from the eye needs slightly more minus power; here the change is small enough to round back to −6.00 D.

Refraction at 13.5 mm, Worn at 12 mm

d = 13.5 − 12 = 1.5 mm = 0.0015 m. For −8.00 D: Fc = −8.00 ÷ (1 − 0.0015 × −8.00) = −8.00 ÷ 1.012 = −7.905 D. The calculation uses the 1.5 mm difference between the two positions, not the 12 mm final distance.

Vertex Distance vs Effective Power

Vertex distance is the physical position of the lens. Effective power is the optical effect of that lens at a given plane, such as the cornea. Changing the vertex distance changes the effective power, which is why a spectacle lens and a contact lens with different labelled powers can give equivalent correction.

Is a Vertex Calculation a Contact-Lens Prescription?

No. The calculation converts power between planes. A contact-lens prescription also specifies parameters such as base curve, diameter and lens material or brand, and is confirmed by assessing how the lens performs on the eye. Treat the calculated value as an optical starting point for a professional fitting.

Common Vertex Distance Mistakes

• Using millimetres in the formula: 12 mm must be entered as d = 0.012.
• Using the new distance instead of the change: from 12 mm to 0 mm, d is 0.012, not 0.
• Dropping the sign: −6.00 and +6.00 move in opposite directions.
• Compensating only the sphere: with astigmatism, compensate both meridians and rebuild the cylinder.
• Assuming every frame sits at 12 mm: use a measured BVD when available.
• Rounding too early: calculate the exact value (e.g. −5.597 D) first and round only the final result. The calculator shows both.

Frequently Asked Questions

Formula and Conversion

How do I convert −6.00 glasses to contacts?

At a 12 mm vertex: −6.00 ÷ (1 − 0.012 × −6.00) = −5.597 D, which rounds to −5.50 D. This is a starting power, not a final contact-lens prescription.

Do I need vertex compensation below ±4.00 D?

Usually the change is smaller than a 0.25 D step. At 12 mm, −3.00 D compensates to −2.896 D, which still rounds to −3.00 D. Higher powers or larger vertex changes produce bigger differences.

Is the vertex distance of a contact lens 0 mm?

Yes. For vertex calculations a contact lens is treated as sitting at the corneal plane, so the new vertex distance is 0 mm.

Contact Lenses and Prescriptions

Why is my contact-lens power different from my glasses power?

Glasses sit in front of the cornea and contact lenses sit on it. The change in position changes the effective power, so stronger prescriptions often need a different contact-lens power.

Does vertex distance affect the cylinder?

Yes. Both principal meridians change, so the compensated cylinder usually differs from the original. The axis stays the same.

Using the Calculator

Which rounding increment should I choose?

Choose the step the lens is supplied in. 0.25 D is the most common. 0.125 D shows a finer step and 0.01 D shows the result to two decimals. The exact value to three decimals is always shown alongside.

Should I always use 12 mm as the original vertex?

No. Use 12 mm only when no measured back vertex distance is available. If you know the actual BVD, enter it instead.

Why does the calculator show a focal-point error?

If 1 − d × Fs is zero or negative, the lens would sit at or beyond its own focal point and no valid compensated power exists. This only happens with extreme combinations of power and distance, so check the inputs.

Important Note

The Vertex Distance Calculator performs optical power conversion only. Results are mathematical starting values. Final spectacle and contact-lens prescriptions, and contact-lens fitting, should be confirmed by a qualified eye-care professional.