Enter 2D coordinates for three soft-tissue landmarks: Glabella (G), Subnasale (Sn) (vertex point), and Soft Tissue Pogonion (Pg'). The calculator returns the angle at Sn and a convexity interpretation.
Glabella (G)
Subnasale (Sn) - Vertex
Soft Tissue Pogonion (Pg')
Educational use only. This tool does not replace clinical diagnosis by a qualified orthodontist or surgeon.
What Is the Facial Convexity Angle?
The facial convexity angle is a profile measurement used in orthodontics, dentofacial analysis, and facial esthetics. A common soft-tissue version uses three points: Glabella (G), Subnasale (Sn), and Pogonion (Pg'), with the angle measured at Sn. In simple terms, it helps describe whether a profile appears more straight, mildly convex, or strongly convex.
How This Calculator Works
This calculator uses coordinate geometry. You provide the x/y location of each landmark from a standardized lateral photograph or cephalometric tracing. It then calculates the angle between vectors Sn→G and Sn→Pg'.
Formula
Angle = arccos[(v1 · v2) / (|v1| × |v2|)] where:
- v1 = G - Sn
- v2 = Pg' - Sn
- v1 · v2 is the dot product
- |v1|, |v2| are vector magnitudes
For convenience, we also show a “convexity from straight line” value: 180° − angle.
How to Use It Correctly
1) Identify landmarks carefully
- G (Glabella): Most prominent point on the forehead soft tissue.
- Sn (Subnasale): Junction of columella base and upper lip.
- Pg' (Soft-tissue Pogonion): Most anterior point of the chin soft tissue.
2) Keep image conditions consistent
Accuracy improves when head posture, camera angle, and scaling are standardized. Inconsistent photos can shift coordinates and alter the result.
3) Interpret as part of a full exam
The facial convexity angle is only one measurement. True diagnosis should include bite relationship, skeletal class, vertical dimensions, and clinical findings.
General Interpretation Guide
- Higher Sn angle (closer to 180°): Straighter profile, lower convexity.
- Mid-range Sn angle: Mild to moderate convex profile.
- Lower Sn angle: More pronounced convexity.
Normative values vary by age, sex, ethnicity, and analysis protocol. Always compare to references that match your population and method.
Common Mistakes to Avoid
- Mixing hard-tissue and soft-tissue landmarks in one calculation.
- Using mirrored or rotated images without coordinate correction.
- Selecting Sn incorrectly (a frequent source of error).
- Treating one angle as a final diagnosis.
Why Clinicians and Students Use This Metric
In orthodontics and facial profile analysis, convexity helps with treatment planning, progress monitoring, and communication. It can be useful when comparing before/after records, documenting growth trends, or discussing profile goals with patients.
Final Note
This facial convexity angle calculator is designed to be quick and practical for learning, screening, and record review. For treatment decisions, rely on full cephalometric analysis and professional clinical judgment.