The curve of Spee and the curve of Wilson are two complementary curvatures that describe the three-dimensional shape of how your upper and lower teeth align when they come together. The curve of Spee runs front to back along the lower arch, creating a gentle upward sweep from the incisors through the molars when viewed from the side. The curve of Wilson runs side to side across the arch, describing the inward tilt of the lower molars and outward tilt of the upper molars when viewed from the front. Together, these curves define the occlusal surface your teeth create for chewing, and they have real consequences for jaw biomechanics, orthodontic treatment planning, and long-term dental health.
What These Curves Actually Look Like
Picture your lower teeth from the side. If you drew a line connecting the tips of the front teeth, the cusps of the premolars, and the cusps of the back molars, that line would not be flat. It dips downward around the premolars, then curves back up toward the last molars, forming a shallow arc. That arc is the curve of Spee. The deepest point of the curve typically sits at the cusp of the second premolar, and in adults with a normal bite, the depth from the deepest point to the flat reference line is roughly 1.5 to 2.5 mm, depending on the individual and the type of bite they have.
The curve of Wilson is harder to visualize because you need to imagine looking at the teeth head-on, slicing through the arch at the molars. The lower molars tilt slightly inward (toward the tongue), and the upper molars flare slightly outward (toward the cheek). Connect the cusp tips across that slice and you get a downward-curving arc. This tilt arrangement keeps the chewing surfaces aligned so that the inner cusps of the upper teeth meet the central grooves of the lower teeth during grinding motions.
In the late 1800s, the German anatomist Ferdinand Graf von Spee first described the anteroposterior curve after studying skulls with heavily worn teeth. He noticed the occlusal line formed an arc that, when extended, would pass through the front edge of the jaw’s condyle (the ball of the jaw joint). Wilson was the first to identify the side-to-side tilt of the grinding teeth, and the coronal-plane curve bears his name. A later concept, Monson’s sphere, tried to unify both curves by proposing that all cusp tips sit on a single sphere with a radius of about four inches (100 mm). Studies have confirmed that the average sphere radius in men is close to that classical value, though individual variation is large enough that a one-size-fits-all sphere does not hold up well across populations.
Why the Curves Exist
These curvatures are not anatomical decoration. They serve a biomechanical purpose tied to how the jaw moves and how force is distributed during chewing. A deeper curve of Spee enhances the force potential for each chewing cycle by maintaining broader contact between upper and lower teeth throughout the jaw’s range of motion, while still permitting the lower jaw to move freely in protrusive and lateral directions.1PubMed Central. The Effect of Accentuation of Curve of Spee on Masticatory Efficiency—A Systematic Review and Meta-Analysis The curve of Spee is closely related to the path the condyle travels along the jaw joint. The plane of occlusion essentially represents the chord of the curve of Spee’s arc, and its angle relative to the condylar path determines how much the teeth separate during forward jaw movement and how tall the cusps can be without interfering.2Indian Journal of Dental Research. Comparative evaluation of the curve of Spee in two age groups and its relation to posterior teeth disclusion
The curve of Wilson plays a complementary role during side-to-side grinding. When you shift your jaw to one side to crush food, the inward tilt of the lower molars and outward tilt of the upper molars helps the working-side teeth stay in contact while the non-working side separates slightly. This separation protects the jaw joint from excessive lateral loads. A steeper curve of Wilson has been associated with a narrower upper arch, and disturbances to this curve can affect how forces reach the temporomandibular joint.
Finite-element modeling has shown what happens when you flatten the curve of Spee artificially. In a study comparing a mandibular model with a normal curve depth of about 2.4 mm against one with a completely flat occlusal plane, the flat model produced higher stress levels throughout the entire mandible. The highest stress at the first molar cusp tip jumped from roughly 3,300 MPa in the curved model to over 5,000 MPa in the flat version.3PubMed Central. Does the flatting of the curve of spee affect the chewing force distribution in the mandible? (3D finite element study) Separate modeling of the jaw joint itself confirmed that stress on the condyle and the articular disc increases as the curve of Spee is reduced.4Advanced Materials Research. A 3D-FEA of Temporomandibular Joint with Reduced Curvature of Curve of Spee The curves, in other words, are shock absorbers. Flatten them and you concentrate force where you do not want it.
How the Curve of Spee Develops
Children are not born with a fully formed curve of Spee. In the primary (baby) dentition, the occlusal plane is essentially flat. The curve begins to take shape when the first permanent molars and lower central incisors erupt, around age six or seven. At that transitional stage, the average maximum depth reaches about 1.3 mm. It then stays relatively stable for several years until the second permanent molars come in around age twelve, at which point the depth increases to roughly 2.2 mm.5PubMed. Development of the curve of Spee The eruption of molars at the back of the arch is the main driver: as they push into position, their cusp tips sit higher relative to the premolars, deepening the arc.
This developmental pattern means that any assessment of whether a child’s curve of Spee is “excessive” needs to account for which permanent teeth have arrived. A curve that seems deep at age eight might be entirely normal for a jaw that has just gained its first molars. Orthodontists typically wait until most permanent teeth are present before making treatment decisions based on curve depth.
How Malocclusion Changes the Curve
The depth of the curve of Spee is not the same across all bite types. Research consistently shows a gradient: people with Class II Division 1 malocclusions (where the upper front teeth protrude significantly) tend to have the deepest curves, while people with Class III malocclusions (where the lower jaw sits forward relative to the upper) tend to have the flattest. One study measured maximum depths of about 2.4 mm in Class II Division 1 subjects versus about 1.8 mm in Class III subjects, with Class I (normal jaw relationship) falling in between.6PubMed. Curve of Spee and its relationship to vertical eruption of teeth among different malocclusion groups This pattern has a direct relationship with the front-to-back position of the jaws: the more the upper jaw sits forward relative to the lower, the deeper the curve tends to be.7PubMed Central. Evaluation depth of the curve of Spee in class I, class II, and class III malocclusion: A cross sectional study
Beyond average depth, the variability matters too. Class I patients tend to show the most consistent curve of Spee values, while Class II and Class III groups display wider scatter, meaning those malocclusion types are more prone to extreme curvature in either direction.8PubMed Central. Correlation between Depth of the Curve of Spee and Some Specific Malocclusion Characteristics in a Population from Sibiu County, Romania—A Cross-Sectional Study For clinicians, this means that diagnosing a deep or flat curve is not just about measuring a number but interpreting it in the context of the patient’s skeletal pattern.
Leveling the Curve in Orthodontics
An excessive curve of Spee is one of the most common problems orthodontists address, particularly in patients with deep bites. Leveling the curve — flattening the occlusal plane closer to even — is a routine part of treatment, but how the leveling actually happens is a bit more nuanced than simply pushing teeth into a straight line.
There are three main mechanisms through which the curve gets reduced:
- Premolar extrusion: The premolars, which sit in the deepest part of the curve, are brought downward (extruded) to fill the dip.
- Incisor intrusion: The front teeth are pushed upward (intruded) to reduce the high point at the front of the arch.
- Incisor proclination: The front teeth are tipped forward, which has the geometric effect of lowering their incisal edges relative to the occlusal plane.
The specific approach depends on the patient’s facial proportions and clinical needs.9PubMed Central. Curve of Spee – from orthodontic perspective In a patient whose lower face is already long, extruding premolars would open the bite further and worsen facial balance, so intrusion of incisors would be preferred. In a patient with a short lower face, premolar extrusion is less cosmetically problematic. A long-term study of patients with Class II Division 1 deep bites treated with continuous archwires found that most of the leveling was accomplished through premolar extrusion, with incisor intrusion playing a secondary role.10PubMed. Leveling the curve of Spee with a continuous archwire technique: a long term cephalometric study
How Much Space Does Leveling Require?
A longstanding clinical rule of thumb holds that you need about 1 mm of extra arch length for every 1 mm of curve depth you want to flatten. Think of it like straightening a curved ribbon: making it flat requires it to become effectively longer, and the teeth need room somewhere in the arch to accommodate that length change.
However, a mathematical model of this relationship showed that the “1 mm for 1 mm” rule actually overestimates the space needed. The true relationship between curve depth and required arch circumference is not linear and is less than one-to-one.11PubMed. Arch length considerations due to the curve of Spee: a mathematical model More recent three-dimensional digital analysis has refined this further, finding that when the depth of the curve at the second molar cusp is less than about 3.5 mm, no additional space may be necessary at all.12PubMed Central. 3D digital space analysis for leveling the curve of Spee This matters practically because overestimating space requirements can lead an orthodontist to extract teeth or expand the arch more than necessary, while underestimating can leave the patient with crowding at the end of treatment.
Long-Term Stability After Leveling
A fair question from anyone undergoing orthodontic treatment is whether the curve just comes back after the braces come off. The evidence here is reassuring. A study tracking patients long-term after curve leveling found that the procedure is relatively stable, and that neither the initial depth of the curve nor the initial amount of crowding predicted how much relapse occurred.13PubMed. Long-term stability of the leveling of the curve of Spee In other words, having started with a particularly deep curve does not doom you to losing the correction.
A more recent retrospective study confirmed this, reporting that non-extraction treatment reduced curve depth at the first premolar from about 1.9 mm to 0.2 mm, with only about 0.1 mm of relapse long-term. Relapse at the second premolar and first molar was even smaller and not statistically significant. Patients who had premolar extractions as part of their treatment may actually fare slightly better at the first molar, showing less clinically meaningful relapse.14PubMed. Long-term stability of curve of Spee depth among orthodontically treated patients: A retrospective longitudinal study
Retention type can also play a role. One comparison of fixed retainers versus removable clear (Essix) retainers found that the fixed retainer group showed some lower incisor extrusion over time, while the Essix retainer, which covers the biting surfaces, prevented this movement and better maintained the leveled curve.15APOS Trends in Orthodontics. Evaluation of long-term stability of curve of Spee levelled with continuous archwires in two different retention protocol If long-term stability of curve leveling is a priority, this is worth discussing with your orthodontist.
The TMJ Connection
Both curves have a relationship with the temporomandibular joint that goes beyond the biomechanical modeling described earlier. Clinical data reveals a somewhat counterintuitive finding: subjects with TMJ clicking or popping sounds tend to have a flatter curve of Spee, not a deeper one. Additionally, a steeper curve of Wilson was associated with a narrower upper arch in patients showing TMJ symptoms.16PubMed Central. The role of occlusal curvatures and maxillary arch dimensions in patients with signs and symptoms of temporomandibular disorders This aligns with the finite-element data showing that flatter curves increase stress on the condyle and disc: the joint is absorbing loads that a properly curved occlusal surface would otherwise distribute across the teeth.
Electromyographic studies have added another dimension, finding that modifications to the curve of Spee alter the patterns of muscular activity during chewing. Flattening the occlusal curve can shift the neuromuscular balance, though the extent varies considerably between individuals. Some people adapt to a flattened curve without symptoms, while others may develop muscle fatigue or discomfort. The clinical takeaway is that aggressive leveling of the curve of Spee, when not clearly indicated, carries real functional trade-offs.
The Curve of Spee and Tooth Wear Over a Lifetime
One natural question is whether the curve of Spee changes as your teeth wear down with age. If the cusps gradually flatten through decades of chewing, does the curve flatten too? The evidence is surprisingly mixed. A study comparing people with normal dentitions to people with significant occlusal wear found no statistically significant difference in curve depth between the groups, suggesting the curve is maintained throughout life even as tooth surfaces change.17PubMed Central. Comparative evaluation of the depth of curve of Spee between individuals with normal dentition and individuals with occlusal wear using conventional and digital software analysis techniques: An in vivo study The likely explanation is that as cusps wear, the teeth compensate by continuing to erupt slightly, a process called continuous eruption or passive eruption, which preserves the overall arc geometry.
However, an archaeological study of heavily worn dentitions told a different story for the molar region specifically: there was no clear indication that the curve of Spee was maintained in the molars once wear became severe.18PubMed. The effects of dental wear on third molar eruption and on the curve of Spee in human archaeological dentitions The discrepancy likely reflects the degree of wear. Modern populations with moderate wear maintain the curve through compensatory eruption, but the extreme wear seen in pre-modern populations (from gritty, unprocessed diets) may overwhelm that compensatory mechanism. For prosthodontists designing restorations for patients with heavily worn teeth, this means the existing occlusal plane may not reflect the patient’s original curve of Spee, and the reconstruction should be designed from first principles rather than simply copying what remains.
Why a Standard Radius Does Not Fit Everyone
Dentists reconstructing missing or damaged teeth — whether with crowns, bridges, or full-mouth rehabilitations — need to rebuild an occlusal surface that mimics these natural curves. For decades, the standard shortcut has been to use Monson’s four-inch (100 mm) radius as a template for both the curve of Spee and the curve of Wilson. While the mean sphere radius across populations does land close to that classical value,19PubMed. Statistical evaluation of Monson’s sphere in healthy permanent dentitions in man the individual variability is substantial, and some populations show systematically different values. A three-dimensional measurement study of an Indian population found that both the curve of Spee and curve of Wilson radii were larger than the 100 mm standard, pointing to ethnic differences in occlusal curvature that a single template cannot capture.20PubMed Central. Analysis of the curve of Spee and the curve of Wilson in adult Indian population: A three-dimensional measurement study
An instrument called the Broadrick flag has long been used in prosthodontics to help reproduce tooth shapes that respect the curve of Spee when designing posterior restorations, specifically to avoid introducing interferences during forward jaw movements.21PubMed. Prosthodontic management of the curve of Spee: use of the Broadrick flag The Broadrick flag is essentially a compass-like device mounted on a semi-adjustable articulator that traces the patient’s individual curve arc, allowing custom cusp heights rather than generic ones. Digital workflows are increasingly replacing this analog tool: three-dimensional scanners can capture the patient’s existing occlusal surface, and software can compute curve parameters directly from the scan data with accuracy within about half a millimeter of manual measurement.22Elektronika ir Elektrotechnika. Measurement of the Depth of Spee’s Curve using Digital 3D Dental Models
An Evolutionary Footnote
The curve of Spee is not unique to modern humans. Fossil hominin mandibles show the same anteroposterior curvature, and researchers have documented a relationship between the curve and facial shape that extends across a wider range of facial morphology than what exists in living people. Specifically, individuals (and species) with more prognathic faces — where the tooth-bearing part of the jaw projects further forward — tend to have a flatter curve of Spee. As the face became flatter over human evolution, the curve deepened.23PubMed Central. Correlation between Depth of the Curve of Spee and Some Specific Malocclusion Characteristics in a Population from Sibiu County, Romania—A Cross-Sectional Study This pattern mirrors what we see in modern malocclusions, where a more retruded lower jaw (as in Class II malocclusion) is associated with a deeper curve. The evolutionary covariation suggests the curve of Spee is not just a dental feature but a structural consequence of how the whole face is built — jaw length, condyle position, and facial projection all shape the arc that teeth trace when they come together.