Vertex Distance, Sagittal Depth & Spherical Equivalent

Vertex Distance, Sagittal Depth & Spherical Equivalent

Quick Answer: Vertex distance changes the effective power of a lens at the corneal plane, so any spectacle Rx over ±4.00 D must be compensated before fitting a contact lens. Sagittal depth (sag) — the height of the lens curve — drives how a soft lens fits; changing diameter or base curve changes sag and tightens or loosens the fit. The spherical equivalent lets you collapse a toric prescription into a single sphere for trial fitting and vertex compensation.

Vertex Distance Compensation

A spectacle lens sits ~12 mm in front of the cornea; a contact lens sits on it. The spectacle's effective power at the corneal plane differs from its labeled power, and the difference grows with lens power. The NCLE standard is to compensate any spectacle Rx ≥ ±4.00 D before prescribing a CL.

Compensation Formula

F_CL = F_spec / (1 - (d × F_spec) / 1000)

where:

• F_CL = contact lens power (D)
• F_spec = spectacle power (D)
• d = vertex distance (mm)

Rules of Thumb

• Minus lenses: lose minus power at the corneal plane → CL power is weaker (less minus) than the spectacle Rx
• Plus lenses: gain plus power at the corneal plane → CL power is stronger (more plus) than the spectacle Rx

Worked Example A: High Myope

Spectacle Rx: −10.00 DS at 12 mm vertex

F_CL = -10.00 / (1 - (12 × -10.00)/1000) = -10.00 / (1 + 0.12) = -10.00 / 1.12 = -8.93 D

Round to the nearest 0.25 D → −9.00 D CL.

The contact lens is weaker (less minus) than the spectacle because the minus lens diverges light, and that divergence has more room to spread by the time it reaches the cornea at the spectacle plane; moving the same correction to the corneal plane requires less minus power.

Worked Example B: High Hyperope / Aphakic

Spectacle Rx: +10.00 DS at 12 mm vertex

F_CL = +10.00 / (1 - (12 × 10.00)/1000) = +10.00 / (1 - 0.12) = +10.00 / 0.88 = +11.36 D

Round to nearest 0.25 D → +11.25 D CL (or +11.50 D, depending on manufacturer steps).

The contact lens is stronger (more plus) than the spectacle because a plus lens converges light toward a focal point behind the spectacle plane; moving the plus correction closer to the eye shortens the effective focal distance, so a stronger plus is required to maintain focus on the retina.

Vertex Conversion Table (12 mm Vertex)

If the vertex distance is not 12 mm (e.g., 10 mm or 14 mm), substitute the measured value into the formula. Larger vertex distances produce larger corrections; smaller vertex distances produce smaller corrections.

Sagittal Depth (Sag)

Sagittal depth is the height (depth) of a contact lens curve measured from the chord (lens diameter) to the apex of the back surface. It is the single most important fitting parameter for soft lenses because it determines how the lens vaults the cornea — a sag mismatch produces a tight or loose fit independent of base curve alone.

Formula

sag = r − √(r² − (D/2)²) ≈ D² / (8r) (small-sag approximation)

where r is the radius of curvature (mm) and D is the lens diameter (mm).

Relationships

Clinical Implications

If a soft lens is too tight (poor movement, compressed fluorescein pattern, injection), you can loosen it by:

• Flattening the base curve (increase radius)
• Reducing the diameter

If a lens is too loose (excessive movement, edge stand-off, discomfort, poor centration):

• Steepen the base curve (decrease radius)
• Increase the diameter

A common fitting mistake is to change only the base curve when the lens is too tight, ignoring diameter. Because sag scales with the square of diameter, a 0.5 mm diameter change can shift sag more than a 0.3 mm base curve change.

Worked Example

A soft CL has base curve 8.6 mm (r = 8.6 mm) and diameter 14.0 mm.

sag ≈ 14.0² / (8 × 8.6) = 196 / 68.8 = 2.85 mm

If the diameter is increased to 14.5 mm with the same base curve:

sag ≈ 14.5² / 68.8 = 210.25 / 68.8 = 3.05 mm

Sag increases by 0.20 mm — a clinically significant tightening of the fit. To preserve the same sag with the larger diameter, the base curve would need to be flattened by approximately 0.3 mm (r ≈ 8.9 mm).

Spherical Equivalent Revisited

The spherical equivalent (SE) condenses a spherocylindrical Rx into a single sphere value. It is used to:

• Select an initial soft CL power when only a spherical lens is available
• Apply vertex compensation to a toric Rx by first computing the SE
• Compare the two eyes for anisometropia magnitude

SE = sphere + (cylinder / 2)

Worked Example

Rx: −2.00 −1.50 × 180

SE = −2.00 + (−1.50 / 2) = −2.00 − 0.75 = −2.75 D

A −2.75 D spherical soft CL will give acceptable distance acuity for low astigmats (residual ≤ 0.75 D); for higher cylinder values, a toric CL is required.

Vertex Compensation of Toric Rx

For high toric Rx, two methods are acceptable:

1. Component method: compensate sphere and cylinder separately using the formula, then keep the original axis
2. SE method: compute SE, compensate SE for vertex, then back-calculate sphere and cyl

Most manufacturers label toric CLs by sphere power, cylinder power, and axis; for high Rx, compensate vertex on each component individually and round to the nearest available step.