Introduction to contact lens diameter, base curve, and sagittal fit
A soft contact lens spans the cornea, crosses the limbus, and lands on the conjunctiva over the sclera. Its fit therefore cannot be understood from the printed base curve alone. The useful geometric comparison is the depth of the eye and the depth of the lens over the same chord. That measurement is called sagittal depth, or sag.
This calculator first selects a practical diameter from the horizontal visible iris diameter (HVID). It then estimates the eye’s sagittal depth across that diameter and solves for a lens base curve that is slightly deeper. The deliberate difference between those depths is the target clearance. A modest clearance tends to support controlled movement; too little can produce bearing and decentration, while too much can produce a tight lens with poor tear exchange.
The result is only a starting estimate. Real lenses with the same printed BC and DIA can behave differently because their materials, thickness profiles, edge designs, optic zones, and peripheral curves differ. Lid forces, tear film, scleral shape, corneal irregularity, and settling also matter. Contact lenses are regulated medical devices, so a licensed optometrist or ophthalmologist must confirm coverage, centration, movement, push-up recovery, comfort, and ocular health.
How to use measured HVID, keratometry, and spectacle power
Use measurements from an examination or topography report rather than guessing. HVID is the visible horizontal iris width in millimetres. Typical adult measurements are roughly 10.5–13.0 mm. The two K readings are the principal corneal meridians in dioptres; a higher K value represents a steeper, smaller-radius cornea. The calculator averages them for its radius model and reports their difference as corneal toricity.
Sphere and cylinder come from the spectacle prescription. They are included so the page can demonstrate vertex compensation at a 12 mm spectacle distance. Pupil size is reported as clinical context because a large pupil can make glare or decentration more noticeable, but it does not alter the geometric calculation. Fit priority changes the target sagittal clearance: comfort uses 0.13 mm, balanced uses 0.20 mm, and optics uses 0.28 mm.
- Enter measured HVID and both K readings in the units printed beside the fields.
- Enter spectacle sphere and cylinder, preserving their positive or negative signs.
- Select pupil size and a fit priority, then calculate the starting specifications.
- Read diameter first because it determines the chord used to solve base curve.
- Compare scenarios by changing one measurement at a time; download the CSV if you need a record.
The contact lens sagittal-depth formulas
Keratometry is converted to an estimated apical corneal radius with the keratometric index 1.3375. If the mean of the two readings is expressed in dioptres, the radius in millimetres is:
The cornea is not treated as a full sphere because it normally flattens toward the periphery. The model uses apical radius and population-average asphericity in the conic sag equation:
Here is half the chord. Beyond HVID/2, the simplified model continues from the limbus along a 38° scleral tangent. This calibration produces a plausible teaching model but does not measure an individual sclera:
Diameter is estimated by adding limbal overlap on both sides of HVID and choosing the nearest stocked size from 13.5, 13.8, 14.0, 14.2, 14.4, or 14.5 mm. The model uses 1.55 mm per side below an HVID of 11.0 mm, 1.20 mm above 12.5 mm, and 1.40 mm otherwise. Large eyes can reach the stocked-diameter ceiling, so a small reported overlap deserves particular clinical attention.
In this diameter formula, is the selected overlap allowance per side. The target is then mapped to the nearest diameter in the calculator’s stocked-size list.
A spherical lens back surface with base curve and diameter has sag . The target is . Inverting that relation gives:
The solved BC is rounded to 0.1 mm and limited to 8.0–9.2 mm. A larger diameter increases lens sag if BC is unchanged, so maintaining the same fit generally requires a flatter, numerically larger BC. This BC–DIA trade-off explains why base curve labels should never be compared without diameter and lens design.
The calculator converts modelled clearance into an estimated post-blink movement using an exponential teaching relationship. The output is constrained to a range of 0–2.5 mm:
This movement relationship is deliberately simple. It helps explain why increasing sagittal clearance tends to reduce movement, but actual movement also depends on material modulus, thickness, edge shape, lid interaction, tear volume, and time allowed for the lens to settle.
For spectacle power, each principal meridian is moved from the spectacle plane to the corneal plane with:
Worked example: 11.8 mm HVID and 43.00 / 43.25 D
Consider HVID 11.8 mm, K readings 43.00 and 43.25 D, sphere −6.00 D, cylinder −0.50 D, and balanced priority. Mean K is 43.125 D, giving an estimated corneal radius of 7.826 mm. The diameter target is 11.8 + 2 × 1.40 = 14.60 mm, which becomes the stocked 14.5 mm diameter.
At that chord, the model estimates ocular sag near 3.580 mm. Adding the balanced 0.20 mm target produces a lens sag of about 3.780 mm. Inverting the sag equation yields a base curve near 8.84 mm, reported as 8.8 mm. Vertex compensation changes the two spectacle meridians from −6.00 and −6.50 D to approximately −5.50 and −6.00 D after quarter-dioptre rounding, producing an illustrative contact lens power of −5.50 −0.50 D.
This does not mean that a 14.5 / 8.8 lens is automatically safe or suitable. It means that this parameter pair is a rational trial starting point under the stated assumptions. A clinician would insert a brand-specific diagnostic lens, allow it to settle, and inspect full corneal coverage, centration, movement after blink, push-up recovery, visual stability, and the ocular surface.
Interpreting the contact lens fitting estimate
Read the reported diameter and actual overlap together. Most disposable soft lenses fall between about 13.8 and 14.5 mm, but a stocked limit can leave a large cornea with less overlap than the raw target requested. Next, check whether BC was clamped. A result at 8.0 or 9.2 mm can signal that the simplified model is outside its useful range rather than that an unusual commercial lens should be ordered.
Clearance is shown in millimetres and micrometres. The expected blink movement is a teaching estimate derived from clearance, not a prediction that can replace observation. Modern soft lenses often show roughly 0.20–0.50 mm of controlled post-blink movement. Excessive movement, edge awareness, decentration, or fluctuating vision can suggest a loose fit. Little movement, poor push-up recovery, conjunctival indentation, trapped debris, or worsening comfort can suggest a tight fit.
Corneal toricity is simply the difference between K1 and K2. Significant cylinder may require a toric lens, but this calculator does not select axis, stabilization design, optic zone, or brand. Spherical equivalent summarizes average spectacle power as sphere plus half the cylinder; it discards axis information and is not a toric prescription.
Limitations and safety of this soft lens estimate
The model assumes a normal aspheric cornea, an average limbal transition, a straight 38° scleral tangent, and a spherical lens back surface. It cannot represent corneal topography, scleral toricity, lens flexure, conjunctival compression, tear-film effects, eyelid forces, irregular astigmatism, keratoconus, corneal grafts, or post-refractive-surgery shape. A flat central K after LASIK may therefore drive the arithmetic toward an unrealistically flat base curve even though peripheral sagittal depth remains closer to normal.
Never use this page to self-prescribe or order contact lenses without a current valid prescription. Remove a lens and seek prompt professional care if you develop pain, increasing redness, light sensitivity, discharge, sudden blur, or reduced vision. These can indicate infection or corneal injury. Proper fitting, hygiene instruction, replacement timing, and follow-up are essential even when a lens feels comfortable.
Sources and assumptions: The keratometric relationship , conic sag equation, and vertex formula are standard ophthalmic-optics relationships. The asphericity, scleral tangent, overlap rules, and clearance targets are teaching constants rather than measurements of your eye.
Sag Match Arcade: tune a safe trial-lens fit
Optional educational game: The eyes and fluorescein patterns below are computed illustrations, not patient images or fitting advice. The game uses the calculator’s diameter, base-curve, sag, overlap, movement, and toricity concepts.
Match five model eyes before the 90-second clinic timer expires. Adjust BC and DIA on the canvas, blink to measure movement, use the push-up test if desired, and commit only when coverage, centration, and movement are acceptable. Correct first attempts build a streak; later eyes introduce steep, wide, toric, and post-surgical geometry.
Eye 1 / 5
Time 90 s
Progress 0 / 5
Streak 0
Base curve 8.60 mm
Diameter 14.0 mm
Ocular sag — mm
Lens sag — mm
Sag clearance — µm
Movement on blink not measured
Decentration — mm
Corneal overlap — mm/side
Tear exchange waiting
Push-up not tested
Score 0
Best 0
Click to play, tune the two tracks, blink, and commit an acceptable fit.
Keyboard: ← and → change BC; ↑ and ↓ change DIA; B or Space blinks; Enter commits. Pointer or touch can drag either track and tap the eye to blink.
- Green pooling — thicker tear layer
- Dark bearing — little or no tear layer
- White-blue ring — lens edge
- Gold band — target movement
- Gold particles — tear debris
- Red ring — excessive tightness