Radius and Diopter Conversion for Corneal Curvature
Why millimeters and diopters describe the same curvature
Corneal curvature is commonly expressed as a radius in millimeters or as an equivalent power in diopters. These are two ways to describe the same surface.
The relationship is inverse: a shorter radius means a steeper cornea and a higher dioptric value. A longer radius means a flatter cornea and a lower dioptric value.
This matters when you are comparing keratometry readings, topography outputs, and contact lens base curves. One device may report a meridian as 45.00 D, while another reports the same curvature as 7.50 mm. Converting between units keeps interpretation consistent across instruments and ordering systems.
The keratometric index and the 337.5 constant
Most clinical keratometers use a standardized refractive index of 1.3375 (the keratometric index) to approximate corneal power from the anterior surface radius. With this convention, the conversion is:
D = 337.5 ÷ r (with r in millimeters)
Example: 7.50 mm corresponds to 45.00 D. Converting the other direction uses the rearranged form:
r = 337.5 ÷ D
This tool uses the 1.3375 convention because it aligns with the SimK style values that are widely used when base curves and curvature are communicated for contact lens fitting and ordering.
How this supports base curve selection and RGP workups
In soft lens fitting, base curve selection is usually not a strict one-to-one match to keratometry. Instead, you choose an initial base curve within the manufacturer’s options and then confirm movement, centration, and comfort on eye. Converting units helps you compare your instrument readings to how trial sets and base curves are labeled.
In RGP fitting, the radius to diopter relationship is foundational for tear lens thinking and base curve adjustments. Converting between millimeters and diopters makes it easier to reconcile K readings, chosen base curve, and the optical implications of steepening or flattening. If you are designing ordered power around a selected fit, pair this with the RGP Calculator.
Important note about instrument differences
Some topographers and tomographers report additional metrics that do not use the keratometric index, such as true net power or total corneal power. These can differ slightly from SimK even when the physical radius is the same. For contact lens ordering and most chairside comparisons, SimK-style values are typically the most compatible with how base curves are labeled.