Free Live Calculators

Vertex Distance Calculator — Glasses to Contact Lens Power

Convert glasses power to contact lens power (or back) using the vertex distance formula, plus the ±4.00 D clinical significance threshold.

Updated
Corrected Contact Lens Power
-9.00 D
Exact (unrounded) value: -8.929 D  ·  rounded to the nearest available 0.25 D step
Vertex correction matters for this prescription. The difference between the two planes is 1.07 D — at or above the ±4.00 D power where the shift is typically large enough to affect the contact lens power that gets ordered.

Corrected Power = F ÷ (1 − d × F), where F is the original lens power and d is the vertex distance in meters. Converting glasses power to contact lens power uses a positive d (moving the correction closer to the eye); converting contact lens power back to glasses power uses the algebraic inverse (moving the correction away from the eye). This is a vertex-distance power conversion only — it does not replace an eye doctor's full contact lens fitting exam, which also accounts for corneal curvature, tear film, and lens material.
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Reference Values

Last verified:
Category Range What It Means Status
Vertex Distance Formula ★ Corrected Power = F ÷ (1 − d × F) F = original lens power in diopters, d = vertex distance in meters. Used to convert a spectacle (glasses) power to the equivalent contact lens power, or a contact lens power back to the equivalent spectacle power. ★ Best
Standard Vertex Distance ★ 12 mm (0.012 m) The most common default vertex distance used for glasses-to-contact-lens power conversions in everyday prescribing. ★ Best
Alternate Vertex Distance 13.5 mm (0.0135 m) A slightly longer vertex distance some practices use as their default, closer to a typical phoropter measurement (about 13.75 mm) or a frame that sits further from the eye. Good
Clinically Significant Threshold ±4.00 D or higher (spectacle power) Above this power, the difference between spectacle and contact lens power is large enough to matter — typically 0.25 D or more, which is the smallest step contact lenses are manufactured in. Okay
Below Threshold Under ±4.00 D (spectacle power) Vertex compensation is usually skipped in practice — the calculated difference is well under 0.25 D, smaller than the smallest available contact lens power step. Good

Source: ODReference.com — Vertex Distance Calculator and Power Chart (Fc = Fs ÷ (1 − d × Fs) formula, standard 12 mm/13.5 mm vertex distances); ODReference.com — Contact Lens Conversion Calculator (±4.00 D clinical significance threshold)

Worked Examples

High Myopia: Glasses → Contacts

Spectacle Power
-10.00 D
Direction
Glasses to contacts
Vertex Distance
12 mm
-9.00 D contact lens power

-10.00 ÷ (1 - 0.012×-10.00) = -10.00 ÷ 1.12 = -8.93 D, rounded to the nearest available 0.25 D step = -9.00 D. Minus powers get weaker (less negative) moving from glasses to contacts.

Moderate Hyperopia: Glasses → Contacts

Spectacle Power
+8.00 D
Direction
Glasses to contacts
Vertex Distance
12 mm
+8.75 D contact lens power

+8.00 ÷ (1 - 0.012×8.00) = +8.00 ÷ 0.904 = +8.85 D, rounded to +8.75 D. Plus powers get stronger (more positive) moving from glasses to contacts — the opposite direction from minus powers.

High Myopia: Contacts → Glasses

Contact Lens Power
-6.00 D
Direction
Contacts to glasses
Vertex Distance
12 mm
-6.50 D spectacle power

-6.00 ÷ (1 + 0.012×-6.00) = -6.00 ÷ 0.928 = -6.47 D, rounded to -6.50 D. Converting the other direction reverses the sign of the vertex distance change, so minus powers get stronger instead of weaker.

Contacts → Glasses at 13.5 mm

Contact Lens Power
+5.00 D
Direction
Contacts to glasses
Vertex Distance
13.5 mm (alternate)
+4.75 D spectacle power

+5.00 ÷ (1 + 0.0135×5.00) = +5.00 ÷ 1.0675 = +4.68 D, rounded to +4.75 D. Using the 13.5 mm alternate vertex distance instead of the 12 mm standard shifts the result slightly — always confirm which vertex distance your prescribing doctor measured.

Low Myopia — Below the Clinical Threshold

Spectacle Power
-2.00 D
Direction
Glasses to contacts
Vertex Distance
12 mm
-1.95 D (difference: 0.05 D)

-2.00 ÷ (1 - 0.012×-2.00) = -2.00 ÷ 1.024 = -1.95 D. The change is only 0.05 D — well under the 0.25 D step contact lenses are manufactured in, so vertex correction is not clinically necessary at this power.

How to Use This Calculator

  1. 1

    Enter your lens power

    Type the spectacle power (for glasses-to-contacts) or the contact lens power (for contacts-to-glasses) in diopters — negative for myopia, positive for hyperopia.

  2. 2

    Choose the conversion direction

    Select "Glasses power → Contact lens power" or "Contact lens power → Glasses power" depending on which number you're starting from.

  3. 3

    Select a vertex distance

    Use the 12 mm standard, the 13.5 mm alternate, or enter a custom distance if your eye doctor measured and recorded a specific vertex distance for your frame.

  4. 4

    Read the corrected power and significance note

    The result shows the exact and rounded corrected power, plus a note on whether the difference is large enough to matter clinically at your prescription strength.

What Each Value Means

Spectacle Power (diopters (D))
The lens power prescribed for glasses, measured at the spectacle plane — typically 12 to 13.5 mm in front of the eye.
Contact Lens Power (diopters (D))
The lens power needed at the corneal plane (directly on the eye) to produce the same focusing effect as the spectacle prescription, once vertex distance is accounted for.
Vertex Distance (millimeters (mm))
The distance between the back surface of a lens and the front of the cornea. This value is the 'd' in the vertex distance formula and directly controls how much the power shifts between glasses and contacts.

Related Calculators

Frequently Asked Questions

What is vertex distance and why does it matter?
Vertex distance is the gap between the back surface of a lens and the front of the eye (the cornea). Glasses sit about 12–13.5 mm in front of the eye, while contact lenses sit directly on it — effectively zero vertex distance. Because lens power is defined at the plane where the lens actually sits, moving a lens closer to or farther from the eye changes how strong it needs to be to produce the same focusing effect at the eye. That's why a glasses prescription and the equivalent contact lens prescription aren't always the same number.
What is the vertex distance formula?
Corrected Power = F ÷ (1 − d × F), where F is the original lens power in diopters and d is the vertex distance in meters. Converting glasses power to contact lens power uses a positive d (the correction is moving toward the eye); converting contact lens power back to glasses power uses the algebraic inverse of that same formula, which is equivalent to using a negative d (the correction is moving away from the eye).
Why does vertex distance correction only matter for higher prescriptions?
The formula's effect scales with how large the original power is — at low powers, the term d × F stays close to zero regardless of direction, so the corrected power barely moves. Clinically, vertex compensation is considered significant starting around ±4.00 D, because below that the shift is usually well under 0.25 D — smaller than the smallest power step contact lenses are manufactured in. A -2.00 D prescription might shift by less than 0.05 D, while a -10.00 D prescription can shift by over 1.00 D.
Why do glasses-to-contacts and contacts-to-glasses conversions go in different directions?
The two conversions are algebraic inverses of each other, not the same calculation run twice. Going from glasses to contacts moves the correction closer to the eye, so minus (myopic) powers get weaker and plus (hyperopic) powers get stronger. Going from contacts to glasses moves the correction farther from the eye, reversing that pattern — minus powers get stronger and plus powers get weaker. Using the wrong direction's formula on the wrong starting power gives an incorrect result, which is why this calculator asks you to select the direction explicitly rather than just guessing from the sign of the power.
Should I use 12 mm or 13.5 mm for vertex distance?
12 mm is the most common default used in everyday contact lens fitting and is a reasonable general-purpose choice. Some practices default to a slightly longer distance (around 13.5 mm), closer to a standard phoropter measurement, or use whatever vertex distance was actually recorded on your specific glasses. If your eye doctor measured and noted an exact vertex distance for your frame, use the custom option and enter that value instead of a preset for the most accurate result.

References & Sources

  1. [1]
    NCBI Bookshelf - Optics and Refraction (opens in new tab)

    Supports: Optical power, refraction, and lens-distance principles.

    Verified

  2. [2]
    American Academy of Ophthalmology - Refractive Errors (opens in new tab)

    Supports: Clinical context for corrective-lens power and refractive error.

    Verified

  3. [3]
    CooperVision - Contact Lens Design and Vertex Conversion (opens in new tab)

    Supports: Practitioner guidance on lens powers, design, and vertex-distance conversion.

    Verified