Sagittal Depth of Contact Lenses

What is the sagittal depth of a contact lens?

Sagittal depth is the perpendicular distance from the centre of a curved surface to the plane its edges circumscribe.

The University of Iowa EyeRounds atlas (Tressa Larson, OD, FAAO; 29 March 2017) states it directly: sagittal depth “refers to the entire contact lens from the center of the lens to the plane that the edges circumscribe.” The same measurement can be taken of the eye or of the lens, which is why the literature uses sagittal height and sagittal depth interchangeably — Contact Lens Spectrum (Lee Hall, May 2015) titles the topic “sagittal height” and computes the same quantity.

Which sagittal depth does a contact lens fitter mean?

The contact lens sense of sagittal depth is the vault of a lens, or of the eye beneath it, over a stated ocular chord. Three other measurements carry the same name and none of them is this page.

• Contact lens sagittal depth — the vault of the lens, or of the cornea and sclera it rests on, over a chord in millimeters. Lens geometry, and the sense this page uses throughout.
• Spectacle lens sag — the same geometry on a different artifact. Retail optical glossaries apply “sag” to a spectacle surface, which sits about 12 mm in front of the eye rather than on it.
• Nasopharyngeal airway depth — an airway measurement, from a different specialty.
• Sagittal imbalance — spinal alignment; craniometry uses the term again.

So a sag figure travels with two labels or it does not travel: which surface, and over what chord. Only the contact lens sense shares a plane with the parameters you order, which is why sag sits beside base curve and diameter rather than beside anything on a glasses Rx.

What is the sagittal depth formula?

The sagittal depth formula for a spherical surface is sag = R − √(R² − (chord ÷ 2)²) — vault as a function of exactly two quantities, a radius of curvature and a chord.

R is the radius of curvature in millimeters and chord is the diameter across which the vault is measured — the lens diameter for a lens, the corneal or scleral chord for an eye. Halve the chord, square the half, subtract it from R², take the root, and subtract that from R. Both inputs are millimeters, so the answer is millimeters. Nothing else enters the spherical form — no power, no material, no brand.

Read it as geometry rather than as a lookup. Hold the chord and steepen the radius, and sag deepens; hold the radius and widen the chord, and sag deepens again. Every published figure further down this page is one of those two moves.

Which sagittal depth formula applies to an aspheric cornea?

Real corneas are not spheres, so the aspheric case uses the conic sagittal depth formula, which adds a shape factor to the same radius and chord. Contact Lens Spectrum gives it as:

sag = ( r − √( r² − p × (chord ÷ 2)² ) ) ÷ p, where p = 1 − e²

r is the apical radius, e is eccentricity, and p is the shape factor. When p = 1.00 the surface is spherical and the conic form collapses back to the spherical one.

Review of Cornea & Contact Lenses (Aaron Zimmerman, OD, MS; Matt Andrew, MS; Melissa D. Bailey, OD, PhD) works a real cornea through that equation: mean K 41.15 D (8.20 mm), corneal diameter 12.10 mm, p calculated at 0.65, giving a sagittal depth of 2.48 mm. Running the same three inputs through the widget above returns 2.47 mm — within 10 µm of the published figure.

Feed those same inputs to the spherical form and you get 2.66 mm, about 190 µm deeper. That gap is the cost of assuming a sphere, and 190 µm is larger than the 100 µm steps some laboratories manufacture in. Use the spherical form to compare two lens surfaces; use the conic form when you have a shape factor for an eye.

Why is sagittal depth meaningless without a chord?

Sag is defined against a chord, so the same surface returns different numbers at different diameters.

Contact Lens Spectrum models a typical eye — HVID 11.90 mm, radius 7.85 mm, eccentricity 0.55 — at a theoretical ocular sagittal height of 3,150 µm. Move the corneal diameter 1 mm either way and the same model returns 2,880 µm at 10.90 mm and 3,510 µm at 12.90 mm: roughly 630 µm across 2 mm of chord.

Asphericity moves it less. Substituting eccentricity 0.30 and 0.70 into the same eye gives 3,275 µm and 3,060 µm — a 215 µm spread. Contact Lens Spectrum notes that about 0.40 mm of radius change is needed to shift that eye by the same amount. Review of Cornea & Contact Lenses reports the same ordering from the lens side: two corneas with similar central K and the same chord, differing only in shape factor, separated by about 200 µm of sagittal depth (its figure caption gives 220 µm at a 12 mm chord).

Citing Young (1992), Contact Lens Spectrum ranks the drivers of ocular sagittal height:

1. Corneal diameter
2. Corneal eccentricity
3. Corneal curvature
4. Scleral radius
5. Scleral eccentricity

Corneal diameter leads. The parameter most fitters never write down is the one that moves sag most. Read Diameter of Contact Lenses for how overall diameter is ordered and labeled.

Why does base curve alone not describe fit?

Base curve is the printed radius. Sagittal depth is that radius and the chord it acts over, which is why two lenses sharing a base curve can vault differently.

The Iowa atlas gives both polarities in one paragraph: “A steeper base curve typically results in increased sagittal depth where a flatter base curve reduces it,” and “larger diameter sclerals typically have deeper sag.” Steeper radius, deeper sag. Larger chord, deeper sag. Change one and hold the other and the vault changes.

The size of that effect is measurable within a single material. Review of Cornea & Contact Lenses, citing van der Worp et al (2021), reports a senofilcon A design supplied in 8.80 mm and 8.40 mm base curves whose sagittal depths differ by 240 µm — the 8.80 mm lens being the shallower. In its published case, an 8.50 mm base curve carried a sag of 3.85 mm while the 9.00 mm option carried 3.47 mm, a difference of nearly 400 µm between two numbers that look half a millimeter apart on a label.

So the printed base curve is a real ordered parameter and it is not a fit prediction on its own. Read Base Curve of Contact Lenses for what BC is, how it is labeled as BC or BOZR, and the empirical flat-K starting bands. That page owns the radius; this one owns the vault.

What corneal and lens sagittal depth values are published?

Published sagittal depth values are only comparable within the same chord and instrument.

Bibby’s 2.74 mm and Hall’s 3,170 µm are not in conflict. They are different chords measured by different means, which is the whole lesson of the row above them. Quote a sag figure without its chord and it stops being a measurement.

The keratoconus row is here to show spread, not to triage disease. An irregular cornea widens the variation by an order of magnitude, and that is a specialty fitting conversation, not a calculator output.

Where does sagittal depth appear in scleral and hybrid designs?

Scleral and hybrid design systems are a different entity from the soft and corneal GP parameters this site converts, and sag is where they touch.

Contact Lens Spectrum describes laboratories that specify designs by sagittal depth rather than by radius, “typically supplied in 100- or 200-micron steps to achieve the required lens vault,” and recommends an initial apical clearance of approximately 400 µm so that a post-lens tear layer of 100–250 µm remains after the lens settles into the conjunctiva. Where a trial lens shows corneal touch, it recommends increasing lens depth by 300–400 µm.

The Iowa atlas puts good scleral clearance at 100–500 µm centrally, notes typical scleral lens thickness of 250–500 µm as a slit-lamp yardstick, and makes the physiological trade explicit: excessive sag “reduces oxygen transmission (think Dk/t where the thickness of the saline layer between the cornea and the lens is t) and reduces BCVA.”

That is the boundary and this page stops at it. We do not fit sclerals, publish laboratory sag tables, or name designs. The clearance that sag produces once the lens is on eye — how it is read on OCT, how it settles, and how the landing zone is aligned — is on Scleral Lens Vault: Central Clearance, Settling, and OCT. For rigid lens geometry and how radius becomes power, read RGP Contact Lens Parameters and Starting Power.

Does lens movement verify sagittal depth?

No. Post-blink lens movement does not correlate with relative sagittal depth, so it cannot be used to confirm the vault.

Review of Cornea & Contact Lenses reports that finding from Andrew et al (2024): the post-blink movement of a soft contact lens showed no correlation to relative sagittal depth, the difference in sag between the cornea and the lens across the same chord length. A deeper lens on a given cornea will not necessarily move less. The article also notes that no device the average practitioner uses outputs a patient’s corneal sagittal depth directly, so the number is calculated or estimated rather than read off a screen.

The practical order is therefore: estimate or calculate sag, choose the trial lens, then confirm the fit on eye and verify power with over-refraction. Movement, lag, centration, and the push-up test belong to that on-eye step and are covered in Contact Lens Fit Assessment, not here. Read Starting Contact Lens Parameters Are Not a Prescription for the bound that applies to every calculator on this site.

Why does spectacle conversion not produce sagittal depth?

Spectacle conversion cannot produce sagittal depth because a glasses Rx contains power, not a radius and not a chord.

A spectacle prescription carries sphere, cylinder, axis, and add. Sag needs three inputs a refraction never held:

• A radius of curvature, in millimeters
• A chord diameter, in millimeters
• A shape factor, if the surface is aspheric

The Contact Lens Conversion Calculator applies vertex compensation past about ±4.00 D, offers spherical equivalent, and rounds to 0.25 D steps. It returns starting power at the corneal plane. It does not return base curve, diameter, or sagittal depth, and no conversion chart can. Calculate power there; calculate sag from geometry here; fit both on eye.

Starting contact lens parameters still require on-eye fit

Sagittal depth narrows the trial lens; it does not end the fitting.

Sag tells you which direction to move when a lens that looks acceptable is uncomfortable. It does not tell you the lens is right, because comfort, tear exchange, centration, and vision are observed on the eye and not computed. Review of Cornea & Contact Lenses is explicit that where a cornea falls outside the normal population distribution, custom options are explored — with a fitter, on eye.

Convert spectacle prescription to contact lens parameters for power. Calculate sagittal depth from radius and chord. Fit base curve and diameter on eye, and verify power with over-refraction after the trial lens. Contact lens parameters at the corneal plane stay unfinished until that sequence is done. Read Contact Lens Parameters for how sag sits beside the rest of the ordered specification.

Sources

Clinical claims on this page are attributed to the publications below.

• University of Iowa, EyeRounds Ophthalmic Atlas — Appropriate Scleral Lens Sagittal Depth(Tressa Larson, OD, FAAO; posted 29 March 2017) — definition as the distance from lens centre to the plane the edges circumscribe; steeper base curve deepens sag and flatter base curve reduces it; larger diameter sclerals have deeper sag; good scleral clearance 100–500 µm centrally; typical scleral lens thickness 250–500 µm; excessive sag reduces oxygen transmission (Dk/t, where t includes the saline layer) and reduces BCVA.
• Contact Lens Spectrum — What You Need to Know About Sagittal Height and Scleral Lenses(Lee Hall, BSc (Hons), PhD, MCOptom, FBCLA; May 2015, vol 30) — conic sag equation with r, p = 1 − e², and d; modelled eye at 3,150 µm with 2,880 / 3,510 µm at 10.90 / 12.90 mm corneal diameter; eccentricity 0.30 / 0.70 giving 3,275 / 3,060 µm; Young (1992) ranking of drivers; Hall et al (2013) 204 normal eyes, corneal 3,170 µm ± 200 and OS15 3,700 µm ± 170; Sorbara et al (2010) OS15 3,740 µm; Sorbara et al (2013) keratoconic 3,410 µm vs normal 2,420 µm; sag-specified designs in 100- or 200-µm steps; ~400 µm initial apical clearance targeting a 100–250 µm post-lens tear layer after settling.
• Review of Cornea & Contact Lenses — The Case for Sagittal Depth in Contact Lens Fitting(Aaron Zimmerman, OD, MS; Matt Andrew, MS; Melissa D. Bailey, OD, PhD) — sag depends on central curvature, asphericity, and corneal diameter; Bibby (1979) population mean 2.74 mm at a 12.0 mm corneal diameter from over 18,000 eyes; worked example at 8.20 mm / 12.10 mm / p 0.65 returning 2.48 mm; van der Worp et al (2021) senofilcon A 8.80 mm vs 8.40 mm base curves differing by 240 µm; a case pair at 3.85 mm (8.50 mm BC) vs 3.47 mm (9.00 mm BC); Andrew et al (2024) showing no correlation between post-blink movement and relative sagittal depth.