7.849
mm
15.698
mm
23.26
mm
31.1
mm
7.849
mm
15.698
mm
23.26
mm
31.1
mm
The Diopter to mm Converter translates between diopter (D) measurements and physical dimensions (radius of curvature and focal length) using the appropriate refractive index. This conversion is fundamental in ophthalmic optics, optometry, and lens design.
The diopter is the unit of measurement for the optical power of a lens or curved mirror, defined as the reciprocal of the focal length in meters: 1 D = 1/f(meters). In ophthalmology, diopters are used to express corneal curvature (keratometry), lens prescriptions, intraocular lens power, and accommodative amplitude.
The conversion between diopters and physical radius depends on the refractive index of the medium. For keratometry, the standard refractive index is 1.3375 (the keratometric index), which is not the true corneal refractive index (1.376) but rather a value adjusted to account for the negative power of the posterior corneal surface. Using this standard, the conversion formula is: Radius (mm) = (n-1) × 1000 / Diopters = 337.5 / D.
Different contexts use different refractive indices: 1.336 for the reduced eye model in physiological optics, 1.49 for CR-39 plastic spectacle lenses, 1.523 for crown glass lenses, and 1.6-1.74 for high-index spectacle lens materials. The higher the refractive index, the thinner a lens can be for the same power, which is why high-index materials are popular for strong prescriptions.
Focal length represents the distance from the lens (or refracting surface) to the point where parallel light rays converge to a focus. In the context of the eye, the cornea has a focal length of approximately 31 mm (in the aqueous/vitreous media), while the total eye has a focal length of approximately 22.3 mm — perfectly matching the axial length in emmetropic eyes.
This converter is useful for ophthalmologists calculating IOL parameters, opticians designing spectacle lenses, researchers working with optical models of the eye, and students learning ophthalmic optics.
The converter uses the lensmaker's equation for a single refracting surface:
Where n is the refractive index of the lens or medium. The 1000 factor converts from meters to millimeters. For keratometry, n = 1.3375 gives the standard formula: radius = 337.5 / K diopters.
The Radius of Curvature is the physical radius of the optical surface in mm. For keratometry, this represents the corneal radius. Focal Length (in medium) is the distance to focus within the refracting medium, while Focal Length (in air) is the standard focal length. Positive values indicate converging (plus) power, negative values indicate diverging (minus) power. For zero diopters (plano), the focal length is infinite.
Inputs
Results
A cornea measuring 43 D has a radius of 7.85 mm. Focal length in the eye's media is 31.1 mm.
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Results
A -4.00 D high-index lens has a radius of 167.5 mm (concave) and focal length of -250 mm in air.
A diopter (D) is the unit of optical power, equal to the reciprocal of the focal length in meters. A +2.00 D lens focuses parallel light at 0.5 meters (500 mm). Positive diopters are converging (for hyperopia), negative are diverging (for myopia).
The keratometric index (1.3375) is a calibration constant, not the true corneal refractive index (1.376). It was chosen to account for the negative power of the posterior corneal surface, so that measuring only the anterior surface gives the total corneal power. Using 337.5/K gives the radius directly.
Radius (mm) = 337.5 ÷ K (diopters). For example, K = 43 D gives radius = 337.5/43 = 7.85 mm. Conversely, K (D) = 337.5 ÷ radius (mm). This conversion is used constantly in contact lens fitting and IOL calculations.
The total eye has a focal length of approximately 22.3 mm in the vitreous (reduced eye model), matching the average axial length. The cornea contributes about +43 D and the crystalline lens about +20 D for a total of about +63 D in an emmetropic eye.
Refractive index (n) is the ratio of the speed of light in vacuum to the speed in a medium. Higher n means light slows more and bends more. Air is ~1.0, water is 1.33, the cornea is 1.376, and spectacle lens materials range from 1.49 to 1.74.
Higher refractive index materials bend light more per unit thickness, allowing lenses to be thinner for the same power. A -8.00 D lens in 1.74 high-index material is about 30-40% thinner than in standard 1.49 plastic, significantly improving cosmetic appearance and comfort.
The thin lens formula assumes negligible thickness (adequate for low-power lenses). For thick lenses (strong prescriptions, IOLs), the actual lens thickness, surface curvatures, and principal planes must be considered for accurate power calculations.
Corneal power is measured by keratometry (manual or automated), which analyzes the reflection of light rings from the anterior corneal surface. Corneal topography provides more detailed maps of the entire corneal surface, and Scheimpflug imaging measures both anterior and posterior surfaces.
Normal keratometry ranges from about 40-47 D, with an average of 43-44 D. Flat corneas (keratoconus suspect: <40 D or post-hyperopic LASIK) and steep corneas (>47 D or keratoconus) are clinically significant and affect contact lens fitting and IOL calculations.
Yes, the formula relates lens curvature to power for any refracting surface. Spectacle lens designers use it with the appropriate material refractive index. However, actual lens design also involves base curve selection, center thickness, and edge thickness considerations.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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