Downs analysis explained: the Frankfort-based skeletal and dental measurements

Simplified Orthodontics Academy · Published 29 October 2026

Key points

The Downs analysis describes a skeletal pattern and a dental pattern on a lateral cephalogram, with Frankfort horizontal (FH) as its horizontal reference [1].
Simplified Ceph computes ten Downs readings: five skeletal (facial angle, angle of convexity, A-B plane, mandibular plane angle, Y-axis) and five dental (cant of the occlusal plane, interincisal angle, lower incisor to the occlusal plane and to the mandibular plane, upper incisor to A-Pog).
Four readings are measured from FH, so a small error in porion or orbitale changes them together.
Downs’ occlusal plane in Simplified Ceph runs from the molar overlap to the midpoint between the incisor tips. It is not the functional occlusal plane used for the Wits appraisal.
Simplified Ceph shows the published reference value next to each reading. This article explains what each reading measures and gives no reference values.

What the Downs analysis is

Downs published his analysis in 1948. It uses FH, the line from porion to orbitale, as its horizontal [1]. Later analyses borrowed from it: Steiner credited some of his readings to earlier authors, among them Downs [2].

Every reading is measured from landmarks, points placed on the radiograph at defined sites [3]. The definitions below are the ones Simplified Ceph uses, so the description matches what the tool measures. Other sources may define a point or a line slightly differently, which is worth knowing before comparing numbers from two programs.

The readings fall into two groups. The skeletal pattern places the chin, the jaws and the mandibular plane against FH and against each other. The dental pattern places the occlusal plane and the incisors against FH, against each other and against the jaws.

The lines

FH (Frankfort horizontal): from porion (Po), the highest point on the upper margin of the external auditory meatus, to orbitale (Or), the lowest point on the lower margin of the orbit.
Facial line: from nasion (N) to pogonion (Pog), the most anterior point of the bony chin.
N-A and A-Pog: from nasion to point A, and from point A to pogonion. Together they form the angle of convexity.
A-B line: from point A to point B.
Mandibular plane: in Simplified Ceph, the line from gonion (Go) to menton (Me).
Y-axis: from sella (S) to gnathion (Gn).
Occlusal plane: from the midpoint of the cusp overlap of the first molars to the midpoint between the upper and lower incisor tips, as Simplified Ceph draws it for this analysis.
Incisor long axes: from the root apex to the incisal edge of the most prominent upper and lower central incisors.

Figure 1. The skeletal lines of the Downs analysis on the Simplified Ceph sample tracing: FH, the facial line N-Pog, N-A and A-Pog, the A-B line, the mandibular plane Go-Me and the Y-axis S-Gn. The mandibular plane meets FH far behind the head, so the angle is shown against a line parallel to FH at gonion. Drawn from the sample’s landmark coordinates; a drawn example, not a patient.

Skeletal pattern

Facial angle: the inner angle where the facial line N-Pog meets FH.
Angle of convexity: 180° minus the angle N-A-Pog at point A. It is 0° when N, A and Pog lie on one straight line, positive when point A lies in front of the line N-Pog, and negative when it lies behind it.
A-B plane: the angle between the A-B line and the facial line N-Pog. It is signed: negative when, going down from A to B, the A-B line slopes further back than the facial line, and positive when it slopes forward of it.
Mandibular plane angle: the angle between FH and the mandibular plane, Go-Me.
Y-axis: the angle between FH and the line S-Gn, measured below FH on the front side.

Dental pattern

Cant of the occlusal plane: the angle between FH and the occlusal plane. It is positive when the plane runs downward from back to front relative to FH.
Interincisal angle: the angle between the long axes of the upper and lower central incisors.
Lower incisor to occlusal plane: 90° minus the angle between the lower incisor axis and the occlusal plane. It is 0° when the incisor stands at a right angle to the plane, and positive when its crown tips forward from that right angle.
Lower incisor to mandibular plane: the angle between the lower incisor axis and Go-Me, minus 90°. It is 0° at a right angle and positive when the crown tips forward.
Upper incisor to A-Pog: the distance from the incisal edge of the upper incisor to the A-Pog line, at a right angle to the line, in millimetres. It is positive when the edge lies in front of the line.

The two lower incisor readings are written as a difference from a right angle, as Simplified Ceph reports them. The ANB and Wits article explains why the choice of occlusal plane matters: Wits uses a different one.

Figure 2. The dental lines of the Downs analysis on the sample tracing: the occlusal plane from the molar overlap to the midpoint between the incisor tips, a line parallel to FH at the molars, the long axes of the upper and lower incisors, the mandibular plane and the A-Pog line with the distance from the upper incisor tip.

Worked example: the sample tracing

Simplified Ceph has a built-in sample tracing (Load a sample tracing). It is a drawn example, not a patient. We computed the Downs readings on it with the tool’s own code, as the tool shows them when the sample is loaded: calibrated, profile facing right.

Reading	Lines	Sample tracing
Facial angle	FH, N-Pog	88.4°
Angle of convexity	N-A, A-Pog	3.4°
A-B plane	A-B, N-Pog	−6.0°
Mandibular plane angle	FH, Go-Me	24.5°
Y-axis	FH, S-Gn	58.2°
Cant of the occlusal plane	FH, occlusal plane	11.9°
Interincisal angle	Incisor axes	131.5°
Lower incisor to occlusal plane	Lower incisor axis, occlusal plane	14.7°
Lower incisor to mandibular plane	Lower incisor axis, Go-Me	2.1°
Upper incisor to A-Pog	A-Pog	5.3 mm

Point A lies in front of the facial line, so the angle of convexity is positive (3.4°). Going down from A to B, the A-B line slopes further back than the facial line, so the A-B plane reading is negative (−6.0°).
The lower incisor makes an angle of 92.1° with Go-Me in this tracing, reported as 2.1°.
The facial angle, 88.4°, uses the same two lines as Ricketts’ facial depth, and the mandibular plane angle, 24.5°, is the same Go-Me to FH angle in McNamara and Ricketts. The interincisal angle appears in Steiner and Ricketts too. The angle is the same; each analysis compares it with its own reference value, because each comes from a different sample.

To see which readings depend on FH, we moved one FH point at a time by 1 mm and left every other point where it was.

Change	Facial angle	Mandibular plane	Y-axis	Cant of occlusal plane	Other six readings
None (sample tracing)	88.4°	24.5°	58.2°	11.9°	as above
Orbitale 1 mm higher	87.7°	25.2°	59.0°	12.6°	unchanged
Porion 1 mm higher	89.2°	23.8°	57.5°	11.1°	unchanged

The four FH readings moved together by about 0.7° each, in opposite directions for the two points, while convexity, the A-B plane and the four incisor readings did not change. When these four readings shift together, the placement of porion and orbitale is worth a second look.

Limits

Landmarks are placed by eye. Porion and orbitale belong to paired structures and can show two outlines; point A, point B and pogonion sit on gentle curves. Two careful people can place a point on a curve in different spots [4]. The cephalometric landmarks article covers identification error.
Which plane. The mandibular plane and the occlusal plane can each be drawn through different points. Compare a reading only with reference values that used the same line.
Reference values come from particular samples. Most reference values come from specific study groups, so read them with the patient’s age, sex and ethnic background in mind.
Check your own error. Tracing a few films again after a while shows how far your own points move [5].
Description, not decision. This article describes the measurements. It does not cover diagnosis or treatment planning.

Do this in Simplified Ceph

Simplified Ceph includes the Downs analysis: the skeletal and dental pattern on the Frankfort horizontal, including the facial angle and the Y-axis. You place the landmarks on a lateral cephalogram, and the readings update as you go. Simplified Ceph shows the published reference value next to each reading. There is a Free plan for lateral cephalometric analysis.

Open Simplified Ceph About Simplified Ceph

Educational content for clinicians and students. Reference values vary between populations. This page does not replace clinical judgement.

References

Downs WB. Variations in facial relationships: their significance in treatment and prognosis. Am J Orthod. 1948;34(10):812-840. doi:10.1016/0002-9416(48)90015-3.
Steiner CC. Cephalometrics in clinical practice. Angle Orthod. 1959;29(1):8-29. Publisher’s page
Jacobson A, Jacobson RL, eds. Radiographic Cephalometry: From Basics to 3-D Imaging. 2nd ed. Chicago: Quintessence; 2006. ISBN 978-0-86715-461-0.
Baumrind S, Frantz RC. The reliability of head film measurements. 1. Landmark identification. Am J Orthod. 1971;60(2):111-127. PMID: 5283996.
Houston WJB. The analysis of errors in orthodontic measurements. Am J Orthod. 1983;83(5):382-390. doi:10.1016/0002-9416(83)90322-6.