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Vision Prescription Converter Calculator
Convert between vision prescription formats including diopters, Snellen, and LogMAR. Plus glasses-to-contacts conversion with vertex distance correction.
⚠️ Medical Disclaimer: This calculator is for educational reference only. Always verify prescription conversions with your eye care provider before ordering glasses or contact lenses.
Glasses Prescription
D
D
°
mm
Transposed (Plus Cylinder Form)
-4.75 / +1.25 × 180°
Original: -3.50 / -1.25 × 90°
Contact Lens SPH⧉
-3.25 D
At vertex 12mm
Contact Lens CYL⧉
-1.25 D
Axis 90°
Approx Snellen⧉
20/200
From SPH only (rough)
Spherical Equivalent⧉
-4.00 D
SPH + CYL/2
Snellen / LogMAR Converter
LogMAR⧉
0.30
20/40
Metric (6m)⧉
6/12
6-meter equivalent
Quick Reference
| Snellen (ft) | Snellen (m) | LogMAR | Description |
|---|---|---|---|
| 20/10 | 6/3 | -0.30 | Excellent |
| 20/15 | 6/4.5 | -0.18 | Better than average |
| 20/20 | 6/6 | 0.00 | Normal |
| 20/25 | 6/7.5 | 0.10 | Near normal |
| 20/40 | 6/12 | 0.30 | Mild loss (driving limit) |
| 20/60 | 6/18 | 0.48 | Moderate loss |
| 20/100 | 6/30 | 0.70 | Severe loss |
| 20/200 | 6/60 | 1.00 | Legal blindness (US) |
| 20/400 | 6/120 | 1.30 | Profound loss |
Planning notes, formulas, and examples
About the Vision Prescription Converter Calculator
The Vision Prescription Converter Calculator helps you convert between different formats used in eye care — diopters, Snellen fractions, and LogMAR (Logarithm of the Minimum Angle of Resolution). It also converts glasses prescriptions to contact lens prescriptions using vertex distance correction, which accounts for the difference in lens-to-eye distance.
Eye prescriptions contain sphere (SPH) for nearsightedness or farsightedness, cylinder (CYL) for astigmatism, and axis for cylinder orientation. Optometrists may write prescriptions using either plus cylinder or minus cylinder form. This calculator can transpose between these notations and apply vertex distance correction for prescriptions ±4.00 diopters or stronger.
Understanding your prescription helps you compare quotes from different providers, order glasses online, and verify that your contact lens prescription is correct relative to your spectacle prescription.
When This Page Helps
Vision prescriptions are written in specialized notation that can vary between practitioners and countries. This converter bridges the gap between Snellen notation (20/20 system), metric Snellen (6/6), LogMAR (used in clinical research), and diopter values. It's also essential when switching between glasses and contacts, since prescriptions differ by the vertex distance — typically 12mm for glasses but 0mm for contacts.
How to Use the Inputs
- Enter your sphere (SPH) and cylinder (CYL) power in diopters, along with the cylinder axis.
- View the converted plus/minus cylinder notation.
- Check the vertex-distance-corrected contact lens equivalent.
- Enter a Snellen fraction to convert to LogMAR and estimated diopters.
- Review the reference table for common Snellen-to-diopter approximations.
- Always verify conversions with your eye care provider before ordering.
Formula used
Cylinder Transposition: New SPH = Old SPH + Old CYL; New CYL = −(Old CYL); New Axis = (Old Axis + 90) mod 180
Vertex Distance Correction: Corrected Power = Power / (1 − d × Power) where d = vertex distance in meters (typically 0.012m)
Snellen to LogMAR: LogMAR = −log₁₀(Snellen fraction), e.g. 20/20 = −log(20/20) = 0.0
Approximate Diopter from Snellen: Diopter ≈ −(denominator − numerator) / denominator (rough estimate)Example Calculation
Result: Contact lens: SPH −3.35 / CYL −1.20 × 90°
With a glasses prescription of −3.50 / −1.25 × 90, vertex distance correction at 12mm gives: SPH = −3.50 / (1 − 0.012 × (−3.50)) = −3.50 / 1.042 = −3.36, rounded to −3.35. CYL is corrected similarly. The minus sign means the correction is less strong for contacts because they sit closer to the eye.
Tips & Best Practices
- Vertex distance correction is only clinically significant for prescriptions over ±4.00 diopters. Under ±4.00, the difference is negligible.
- Contact lens prescriptions also include base curve (BC) and diameter (DIA) — these cannot be derived from glasses prescriptions and must be fitted by your optometrist.
- Add power (near correction) for progressive or bifocal lenses is the same for both glasses and contacts.
- Snellen 20/20 is considered "normal" vision but NOT perfect vision. Many people achieve 20/15 or even 20/10 with correction.
- LogMAR is preferred in clinical research because it provides equal spacing between lines on the letter chart, making statistical analysis more valid.
- Your right eye (OD — oculus dexter) and left eye (OS — oculus sinister) may have different prescriptions.
- Prescriptions typically expire after 1–2 years. Changes of 0.25–0.50 diopters are normal between exams.
Understanding Diopter Values
A diopter (D) is the unit of measurement for lens power. It equals the reciprocal of the focal length in meters: 1D = 1/1m focus. Negative diopters correct myopia (nearsightedness) by diverging light rays. Positive diopters correct hyperopia (farsightedness) by converging light rays. Most prescriptions fall between −20.00D and +20.00D, with the majority between −8.00D and +6.00D.
Vertex Distance Explained
Vertex distance is the space between the back surface of a lens and the front of the cornea. For glasses, this is typically 12–14mm. For contact lenses, it's essentially zero. The vertex distance correction formula adjusts the lens power to account for this difference. The correction is more significant for higher prescriptions because the focal point shift becomes more pronounced at greater distances.
Astigmatism and Cylinder Power
Astigmatism occurs when the cornea or lens has two different curvatures (like a football rather than a basketball). The cylinder value measures the difference between the steepest and flattest meridians. Regular astigmatism is correctable with spectacles or toric contact lenses. Irregular astigmatism (from keratoconus, scars, or surgery) may require rigid gas permeable lenses or specialty contacts.
Sources & Methodology
Last updated:
Methodology
This page performs three reference conversions: cylinder transposition between plus and minus cylinder form, spectacle-to-contact starting-power adjustment with a vertex-distance formula, and visual-acuity conversion between Snellen notation and logMAR. The transposition math is exact, while the contact-lens and Snellen-to-diopter outputs are starting estimates meant to help the user understand notation rather than to replace a fitted prescription.
The result is not a contact lens prescription generator. Base curve, diameter, corneal shape, tear film, brand-specific lens availability, and clinical refraction still determine the final prescription an eye care professional dispenses.
Sources
- Evaluation of Visual Acuity (NCBI Bookshelf / StatPearls) — Reference for Snellen, decimal, and logMAR notation relationships in clinical visual-acuity measurement.
- Visual Acuity (NCBI Bookshelf / Webvision) — Background on Snellen notation, minimum angle of resolution, and logMAR scaling.
- Clinical importance of accurate refractor vertex distance measurements prior to refractive surgery (PubMed / Journal of Refractive Surgery) — Clinical optics reference showing why vertex distance matters more as refractive power increases.
Frequently Asked Questions
SPH (sphere) corrects myopia (minus values) or hyperopia (plus values) and is measured in diopters. CYL (cylinder) corrects astigmatism — an irregularly shaped cornea. Axis is the angle (1–180°) that orients the cylinder correction. If your CYL is zero or blank, you have no astigmatism and axis is not needed.
They describe the same prescription in different notation. Minus cylinder is used by optometrists; plus cylinder is used by ophthalmologists. To convert: add the old CYL to the old SPH for the new SPH, negate the CYL, and rotate the axis by 90°. Example: −2.00 / −1.00 × 180 becomes −3.00 / +1.00 × 90.
Glasses sit about 12mm from your eye, while contacts sit directly on the cornea. This difference in distance (vertex distance) means the lens power needed is slightly different — typically less strong for contacts with minus prescriptions and more strong for plus prescriptions. The stronger the prescription, the larger the difference.
LogMAR (Logarithm of the Minimum Angle of Resolution) is a visual acuity scale where 0.0 equals 20/20 (Snellen), negative values are better than 20/20, and positive values are worse. It's preferred in clinical research because each 0.1 step represents the same optical change, unlike Snellen where the steps are unequal. LogMAR 0.3 = 20/40; LogMAR 1.0 = 20/200.
Not directly. Contact lenses require a separate fitting that determines base curve and diameter in addition to power adjustments. For prescriptions under ±4.00D the power may be essentially the same, but a contact lens exam is still required for proper fit. Using the wrong base curve can cause corneal damage.
20/20 means you see at 20 feet what a person with normal vision sees at 20 feet (using the imperial system). 6/6 is the metric equivalent using meters. 20/40 means you need to be at 20 feet to see what a normal eye sees at 40 feet. In many countries, 6/6 (meters) is the standard; in the US and Canada, 20/20 (feet) is used.
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