Optics
Contacts and glasses are not the same number
A lens twelve millimetres in front of your eye does not do the same job as one sitting on it. Above about four dioptres the difference is a quarter of a dioptre or more, and it goes in opposite directions for plus and minus.
The conversion updates as you type.
- Starting power
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- Equivalent power
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- Before rounding
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- Difference
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This is the optical equivalent only. A contact lens prescription also specifies base curve, diameter and product, which come from a fitting.
What vertex distance is
The distance from the back surface of a spectacle lens to the front of your cornea. Conventionally taken as twelve millimetres, though it varies with how a frame sits on a particular face, and some practices measure it individually for strong prescriptions.
A contact lens sits at zero. That is the whole of the difference, and it is enough to change which lens gets made.
The formula
F′ = F ÷ (1 − dF), with d in metres and F in dioptres. Going from the spectacle plane to the cornea, d is positive; going the other way it is negative.
Work a case through. A −8.00 spectacle lens at twelve millimetres: the denominator is 1 − (0.012 × −8) = 1.096, so the corneal-plane power is −8 ÷ 1.096 = −7.30, which rounds to −7.25. Three quarters of a dioptre weaker, and that is three steps on a lens that is made in quarter-dioptre increments.
Now the same at +8.00: the denominator is 1 − 0.096 = 0.904, giving +8.85, rounding to +8.75. Three quarters of a dioptre stronger. The two directions are opposite, which is the part people get wrong when they try to remember a rule of thumb instead of running the arithmetic.
Why it barely matters below four dioptres
The compensation scales roughly with the square of the power. At −2.00 the shift is about 0.05 D. At −4.00 it is around 0.19 D, still under the 0.25 D step lenses are made in. At −6.00 it reaches 0.42 D and starts changing the lens. By −12.00 it is 1.5 D, which is not a rounding matter at all.
This is why most people wearing mild prescriptions find their contact and spectacle numbers identical and assume conversion is unnecessary. It is unnecessary, for them.
Conversion chart at 12 mm
| Glasses | Exact | Contacts |
|---|---|---|
| −1.00 | -0.99 | −1.00 |
| −2.00 | -1.95 | −2.00 |
| −3.00 | -2.90 | −3.00 |
| −4.00 | -3.82 | −3.75 |
| −5.00 | -4.72 | −4.75 |
| −6.00 | -5.60 | −5.50 |
| −7.00 | -6.46 | −6.50 |
| −8.00 | -7.30 | −7.25 |
| −9.00 | -8.12 | −8.00 |
| −10.00 | -8.93 | −9.00 |
| −12.00 | -10.49 | −10.50 |
| Glasses | Exact | Contacts |
|---|---|---|
| +1.00 | 1.01 | +1.00 |
| +2.00 | 2.05 | +2.00 |
| +3.00 | 3.11 | +3.00 |
| +4.00 | 4.20 | +4.25 |
| +5.00 | 5.32 | +5.25 |
| +6.00 | 6.47 | +6.50 |
| +7.00 | 7.64 | +7.75 |
| +8.00 | 8.85 | +8.75 |
What this does not replace
Power is one line of a contact lens prescription. The others are not optional details.
Base curve describes the curvature of the lens, and it has to match the curvature of your cornea closely enough that the lens moves a little with each blink but does not slide. Too flat and it moves excessively and falls out; too steep and it grips, cutting off the tear exchange underneath it. Diameter governs how far the lens extends past the cornea. Material and replacement schedule determine how much oxygen reaches the eye over a day of wear.
None of that can be derived from a spectacle prescription, which is why contact lenses require their own prescription in most jurisdictions and why a fitting involves someone looking at the lens on your eye with a slit lamp.
This tool performs a standard optical conversion on a number you supply. It is not a contact lens prescription and is not a substitute for a contact lens fitting. Wearing lenses of the wrong curvature or material can damage the cornea.
Related: read your full prescription, or measure your pupillary distance.
Questions people ask
- Why is my contact lens power different from my glasses power?
- Because distance from the eye changes what a given power does. A spectacle lens sits about twelve millimetres in front of the cornea; a contact lens sits directly on it. Minus powers become weaker at the corneal plane and plus powers become stronger. Below about four dioptres the difference is too small to change the lens that gets made, which is why most people never notice.
- Can I order contact lenses using this number?
- No. Power is only one of several things a contact lens prescription specifies. Base curve and diameter determine how the lens sits and moves on your eye, and they come from a fitting where a clinician looks at it on you. A lens with the correct power and the wrong curve can abrade the cornea. This tool exists so the numbers make sense, not so you can order from them.
- What vertex distance should I use?
- Twelve millimetres is the conventional assumption and what most charts are built on. If you know your own — some practices measure it, particularly for strong prescriptions — use that instead. At high powers a two millimetre difference in assumed vertex distance can move the result by a quarter dioptre.
- Does this apply to astigmatism as well?
- The same compensation applies to each principal meridian, so a strong cylinder is affected too. In practice that means converting both the sphere and the sphere-plus-cylinder figure and working back, which is a step beyond what this tool does. For toric contact lenses in a strong prescription, this is the fitter's job rather than a calculator's.
- Why do plus lenses get stronger and minus lenses weaker?
- It follows directly from F prime equals F divided by one minus dF, where d is the vertex distance in metres. Moving a converging lens closer to the eye reduces its effective power, so a stronger one is needed at the cornea. Moving a diverging lens closer increases its effective power, so a weaker one suffices. The effect scales with the square of the power, which is why it is invisible at low powers and substantial at high ones.