Corneal Radius to Dioptre Converter
Corneal Radius to Dioptre Converter
K = 337.5 ÷ r, both ways, where 337.5 is (1.3375 − 1) × 1000 and 1.3375 is a convention rather than the cornea’s refractive index. A 7.5 mm cornea is 45.00 D exactly — at that index.
Radius (mm) ⇄ keratometric power (D)
Keratometric indexA 7.80 mm anterior radius at the Javal index of 1.3375, with 43.00 D entered for the inverse
The conversion, and what the index in it assumes
- 337.5, exactly
- (1.3375 − 1) × 1000. Both sources read print the pair “r(mm) = 337.5 / K” and “K = 337.5 / r(mm)”, and one of them states that “the corneal refractive index used by most keratometers is 1.3375, which is why 337.5 appears in conversion formulas”. The relation is a pure reciprocal, which is why this is a formula page and not a unit converter: no multiplicative factor can express it
- what the premise is worth, computed
- the ratio that premise asserts is published as the anterior radius being “on average, 1.21 times greater than the posterior radius”. Put that into a two-surface cornea — anterior power (1.376 − 1)/r, posterior power (1.336 − 1.376)/(r ÷ 1.21) — and the single index that would reproduce the total comes out at 1.3276, INDEPENDENT of the radius, which is the one thing the premise genuinely delivers. It is not 1.3375. The raytraced study read for this page back-calculates 1.3317 ± 0.0017 from OCT data, which sits between the two
- the instrument spread, computed
- at a 7.7 mm radius the Javal index reports 43.83 D and the Zeiss index 43.12 D: a difference of 0.714 D on one cornea. The paper read gives the average difference as “around 0.75 dioptres” and a worst case of 1.67 D between the 2.5% and 97.5% quantiles of its back-calculated index. The gap is LARGER on a steep cornea than a flat one — 0.81 D at 6.8 mm against 0.66 D at 8.4 mm — because it is a difference of reciprocals and not a constant offset
- where the premise breaks
- corneal refractive surgery reshapes the anterior surface and leaves the posterior one, so the 1.21 ratio is destroyed. The source read states that “this ratio is disrupted, and the keratometric refractive index becomes invalid”, that after myopic correction “keratometry (K) readings usually overestimate corneal power” while hyperopic correction under-states it, and that “the higher the attempted correction, the higher the resulting under- or overcorrection”. NO DIOPTRIC FIGURE IS PRINTED FOR THAT ERROR, because that source gives none: it says only that the index “should be decreased proportional to the amount of correction” without stating the proportion, and no second source read supplied one. The dioptric figures above are between two INDICES on an unoperated cornea, which is a different quantity
Worked example
A 7.80 mm anterior radius at the Javal index of 1.3375, with 43.00 D entered for the inverse
(1.3375 − 1) × 1000 = 337.5, which is where the constant comes from and is exact in decimal
337.5 ÷ 7.80 = 43.27 D
At the Zeiss index. 332 ÷ 7.80 = 42.56 D, which is 0.705 D flatter for the same cornea. Neither reading is wrong; they are different conventions applied to one measurement
The inverse. 337.5 ÷ 43.00 = 7.849 mm. At the Zeiss index the same 43.00 D would be a 7.721 mm cornea — a 0.13 mm difference, which is more than a keratometer's repeatability
The anchor. 337.5 ÷ 45.00 = 7.500 mm exactly, both ways — at the Javal index and nowhere else
What the convention assumes, computed. A cornea whose anterior radius is 1.21 times its posterior one, with the published 1.376 and 1.336 indices, needs a single equivalent index of 1.3276 — not 1.3375 — and that figure is the same at 6.8, 7.5 and 8.4 mm, which is the whole content of a “constant and linear relationship”
Where it refuses. Enter a radius of zero and no answer appears: a flat surface has no dioptric power, and the division is undefined rather than large
The same cornea at four indices, and what the choice costs
| Radius (mm) | 1.3375 Javal (D) | 1.336 aqueous (D) | 1.332 Zeiss (D) | 1.3317 raytraced (D) | Javal less Zeiss (D) |
|---|---|---|---|---|---|
| 6.80 | 49.63 | 49.41 | 48.82 | 48.78 | 0.809 |
| 7.00 | 48.21 | 48.00 | 47.43 | 47.39 | 0.786 |
| 7.20 | 46.88 | 46.67 | 46.11 | 46.07 | 0.764 |
| 7.50 | 45.00 | 44.80 | 44.27 | 44.23 | 0.733 |
| 7.70 | 43.83 | 43.64 | 43.12 | 43.08 | 0.714 |
| 7.80 | 43.27 | 43.08 | 42.56 | 42.53 | 0.705 |
| 8.00 | 42.19 | 42.00 | 41.50 | 41.46 | 0.688 |
| 8.40 | 40.18 | 40.00 | 39.52 | 39.49 | 0.655 |
What a keratometer measures and what it reports
| Quantity | Measured or assumed | Where it comes from |
|---|---|---|
| Anterior corneal radius | MEASURED, from the size of a reflected image | The instrument’s only optical measurement |
| Keratometric index, 1.3375 | ASSUMED, and usually hard-coded | A convention chosen so one surface stands in for two |
| Posterior corneal radius | ASSUMED, as a fixed ratio to the anterior | Published as 1.21 preoperatively; not measured by a keratometer |
| Posterior corneal astigmatism | ASSUMED at 0.15 ± 0.10 D | Measured directly at 0.31 ± 0.14 D in normal corneas |
| Corneal thickness | NOT USED at all | Which is why a raytraced index differs from the convention |
| Reported power in dioptres | COMPUTED, from the one measurement and the assumptions above | This page’s arithmetic |
A keratometer measures a radius and reports a power, and the bridge is a convention
The arithmetic on this page is one division, and it is reversible: the keratometric power in dioptres is (nK − 1) × 1000 divided by the anterior corneal radius in millimetres, and the radius is the same division the other way. At the index essentially every instrument applies, 1.3375, the numerator is 337.5 exactly, so a 7.5 mm cornea is reported as 45.00 D and a 43.00 D cornea has a 7.849 mm radius. Both sources read for this page print the pair, and the relation is a pure reciprocal — which is why it cannot be a unit converter with a multiplying factor and has to be a formula.
The interesting part is the index. 1.3375 is not the cornea’s refractive index, which is about 1.376; nor is it the aqueous’s, which is about 1.336. The posterior corneal surface sits between those two and therefore carries negative power, and a keratometer never sees it. 1.3375 is a single number chosen so that measuring one surface reports roughly the power of both, and it rests on the premise that the two curvatures keep a constant relationship. Put the published version of that premise — an anterior radius 1.21 times the posterior — through a two-surface cornea and the equivalent single index comes out at 1.3276, the same at every radius. A study that back-calculated the index by raytracing from optical coherence tomography got 1.3317 ± 0.0017. Neither is 1.3375.
So the convention runs about half a dioptre to three quarters of a dioptre high, and instruments do not even agree on it: the same paper names a Zeiss index of 1.332 alongside the Javal 1.3375, and notes that the conversion is usually hard-coded so a user cannot change it. On a 7.70 mm cornea those two report 43.83 D and 43.12 D, a gap of 0.714 D, which is that paper’s “around 0.75 dioptres on average”. The gap is bigger on a steep cornea and smaller on a flat one, because reciprocals do not shift by a constant. A corneal cylinder, being a difference of two powers at one index, barely moves — about 0.02 D on a 1.50 D cylinder — which is why keratometric astigmatism travels between instruments when keratometric power does not.
The consequence worth the page is what happens when the premise fails. Myopic refractive surgery flattens the front surface and leaves the back one, so the fixed ratio is destroyed and, in the words of the source read, “the keratometric refractive index becomes invalid”: keratometry then over-states corneal power, and the error grows with the correction attempted. That is why intraocular lens formulas fed a keratometric K after LASIK leave patients hyperopic, and why this category contains no lens power calculator. This page prints no dioptric figure for that error, because the source gives none and the proportion it says the index should be reduced by is not stated anywhere that was read. For the readings themselves and the cylinder between them, see corneal astigmatism from keratometry; for the single number a refraction is summarised by, the spherical equivalent.
Frequently asked questions
How do I convert corneal radius in millimetres to dioptres?
Divide 337.5 by the radius in millimetres, and the inverse is the same division the other way. 7.5 mm is 45.00 D and 7.80 mm is 43.27 D. The 337.5 is (1.3375 − 1) × 1000, where 1.3375 is the keratometric index; at a different index the numerator changes, to 332 at 1.332 for instance.
Why is the keratometric index 1.3375 when the cornea’s index is 1.376?
Because 1.3375 was never meant to be the cornea’s index. A keratometer sees only the front surface, and the back surface — between a 1.376 cornea and a 1.336 aqueous — carries negative power. 1.3375 is one number chosen so a front-surface measurement reports approximately the whole cornea’s power, on the assumption that the two curvatures keep a fixed ratio.
Do all instruments use 1.3375?
No. The paper read for this page names a Zeiss index of 1.332 alongside the Javal 1.3375, notes that the conversion is often hard-coded so the user cannot change it, and back-calculates a mean index of 1.3317 by raytracing. On a 7.70 mm cornea 1.3375 and 1.332 report 43.83 D and 43.12 D — 0.714 D apart for the same cornea.
Why do IOL formulas fail after LASIK?
Because the keratometric index assumes a constant ratio of anterior to posterior corneal curvature — the anterior radius being about 1.21 times the posterior — and myopic ablation flattens the front surface while leaving the back one. The source read states that the ratio is then disrupted and the index “becomes invalid”, so keratometry over-states corneal power. It gives no figure for how much, and none is printed here.
Does the index matter for corneal astigmatism?
Hardly at all. Astigmatism is a difference of two powers at one index, so most of the convention cancels: a 1.50 D cylinder at 1.3375 is about 1.48 D at 1.332, where the individual powers move 0.70 D.
Related calculators
References
- Open Exam Prep. Keratometer / Ophthalmometer: Calibration, Readings and Interpretation, Certified Lens Register study guide. open-exam-prep.com. Accessed 10 October 2026.
- Optician’s Friend. Optics Study Guide. opticiansfriend.com. Accessed 10 October 2026. (The page states that its information may contain mistakes and should be independently verified, so every formula taken from it here is corroborated from a second source.)
- Langenbucher A, et al. Back-calculation of keratometer index based on OCT data and raytracing. Acta Ophthalmol. 2021;99:843-9. (Names the Javal index as 1.3375 and the Zeiss index as 1.332, and back-calculates a mean index of 1.3317 ± 0.0017 over the range 1.3233 to 1.3390.)
- Ueno Y, Hiraoka T, Miyazaki M, Ito M, Oshika T. Corneal thickness profile and posterior corneal astigmatism in normal corneas. Ophthalmology. 2015;122(6):1072-8.
- IOL Power Calculation After Refractive Surgery. Cataract & Refractive Surgery Today, crstoday.com. Accessed 10 October 2026.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/