Lateral Centre-Edge Angle Calculator (Wiberg)
Lateral Centre-Edge Angle Calculator (Wiberg)
Wiberg’s lateral centre-edge angle from the two distances that define it, with Hanson’s published thresholds — and the 4 degrees that separate the bony rim from the sourcil, which reclassified ten of fourteen dysplastic hips.
Lateral centre-edge angle of Wiberg
Arctangent from a vertical referenceAn AP pelvis: the lateral acetabular reference point lies 14 mm lateral to and 24 mm above the centre of the best-fit femoral head circle
An arctangent measured from the vertical
— from the centre of the femoral head, between a vertical reference line and a line to the lateral acetabular point
- the horizontal distance is on TOP
- because the angle is measured away from a VERTICAL reference. Transposing the two gives the complement: a normal hip at 30 degrees reads 60 degrees transposed, which looks like gross over-coverage and throws no error. This site’s acetabular index and Sharp angle pages put the vertical distance on top instead, because both of those are measured from a HORIZONTAL reference — three angles on one radiograph, two different orderings
- which vertical line
- the sources disagree. Radiopaedia says the first line runs “vertically along the longitudinal axis of the pelvis”; Radsource draws it perpendicular to the teardrop line through the femoral head centre. On a well-positioned AP pelvis these nearly coincide; on a tilted or rotated one they do not, and the measured angle follows whichever was used
- which lateral point, and what it costs
- Wiberg’s original runs to the lateral acetabular rim; Ogata’s modification runs to the lateral edge of the sourcil, “proposed to be a more functional method given that this measurement includes the weight-bearing portion”. Radiopaedia states the rim method “overestimates coverage by ~4 degrees compared to the acetabular sourcil method” because it includes non-weightbearing bone at the labral base, and Hanson measured the same 4 degrees with 95% limits of agreement from minus 2 to plus 10 degrees
- a reliable measurement of two different things
- Hanson’s inter-observer agreement was “almost perfect for all radiographic measurements: bone LCEA = 0.92, sourcil LCEA = 0.92”. Both methods are highly reproducible; they are reproducibly measuring different quantities, which is why 46 of 188 hips (24%) differed by more than 5 degrees between them
- derivation
- Wiberg G, 1939, for the angle; the thresholds used here are Hanson JA et al, J Hip Preserv Surg 2015;2(3):280-286, read in full. Wiberg’s monograph was not reachable, so no sentence is attributed to it
Worked example
An AP pelvis: the lateral acetabular reference point lies 14 mm lateral to and 24 mm above the centre of the best-fit femoral head circle
Lateral centre-edge angle = arctan(14 / 24) = arctan(0.5833) = 30.3 degrees, inside Hanson's normal band of above 25 and up to 40 degrees
Transpose the two distances: arctan(24 / 14) = 59.7 degrees, which is the complement and reads as gross over-coverage. Nothing in the arithmetic objects. 30.3 and 59.7 sum to exactly 90, which is the identity this page's proof uses to detect a swap — and it only works away from the point where the two distances are equal, because there both orderings give 45
Take the landmark question instead of the arithmetic one. If the 14 mm was measured to the bony rim, Hanson's mean offset puts the sourcil angle near 26.3 degrees — still normal, but one degree from borderline
A hip with the same 24 mm vertical offset but only 8 mm horizontally gives arctan(8 / 24) = 18.4 degrees, below Hanson's dysplastic threshold of 20 degrees; at 9 mm it is 20.6 degrees and borderline instead. One millimetre of landmark disagreement moves this hip across a published boundary
And at 22 mm horizontally: arctan(22 / 24) = 42.5 degrees, over-covered on Hanson's threshold of above 40 degrees — or 38.5 if that 22 mm was a bony rim measurement and the sourcil sits 4 degrees lower
Hanson’s thresholds, and the inequalities exactly as published
| Band | As Hanson et al state it | Corroboration |
|---|---|---|
| Dysplastic | “<20 degrees” | Radsource: “a center edge angle of less than 20 degrees is consistent with DDH”, with “a lower range of 18 degrees proposed by some surgeons” |
| Borderline dysplastic | “≥20 degrees and ≤25 degrees” | Radsource: “an angle of 20-25 degrees represents borderline dysplasia of the hip (BDH)” |
| Normal | “>25 degrees and ≤40 degrees” | Radsource: “The normal center edge angle is considered to be >25 degrees” |
| Over-covered | “>40 degrees” | Wikipedia’s adult hip table: “>40 degrees indicates overcoverage”, unattributed there |
Bony rim or sourcil: the same hip, two numbers
| Finding | Figure | Cohort |
|---|---|---|
| Mean difference between methods | The bone angle was “4 degrees (95% limits of agreement = minus 2 to 10 degrees) greater than the sourcil” angle | 188 preoperative AP pelvis radiographs, Hanson et al 2015 |
| How often they differ enough to matter | “Forty-six subjects (46/188, 24%) had a LCEA difference greater than 5 degrees between methods” | The same 188 |
| How often they disagree on the category | Of “the 14 subjects with a sourcil LCEA <20 degrees (dysplastic), only four had a bone LCEA also <20 degrees” | The same 188 |
| Independent statement of the same offset | “The lateral acetabular rim method overestimates coverage by ~4 degrees compared to the acetabular sourcil method” | Radiopaedia, attributing the sourcil modification to Ogata et al |
| Reliability of each method | Inter-observer agreement “bone LCEA = 0.92, sourcil LCEA = 0.92” | Hanson et al 2015 |
Two distances, one arctangent, and the landmark that decides it
The lateral centre-edge angle is Wiberg’s measure of how far the acetabulum covers the femoral head laterally. Radiopaedia’s construction is to fit a circle to the inferior and medial margins of the femoral head, then measure between two lines from its centre: one vertical, one running to the lateral acetabular point. A reader who has drawn that circle has two distances rather than an angle, which is what this page takes. Because the reference line is vertical, the horizontal offset is the numerator — the opposite ordering from the acetabular index and Sharp’s angle on this site, which are both measured from a horizontal reference.
The thresholds here are Hanson’s, reproduced with their original inequalities: below 20 degrees dysplastic, 20 to 25 inclusive borderline dysplastic, above 25 and up to 40 normal, above 40 over-covered. They were applied to 188 adults awaiting hip arthroscopy for suspected pathomorphology, which is a symptomatic surgical cohort rather than a population sample. Radsource states the same three boundaries independently and records that some surgeons use 18 degrees instead of 20.
The reason Hanson’s paper exists is the interesting part. The lateral point can be the bony acetabular rim, as Wiberg drew it, or the lateral edge of the sourcil, as Ogata’s modification does, on the argument that the sourcil is the weight-bearing part. Those are not interchangeable. Hanson measured the bony angle 4 degrees greater on average, with 95% limits of agreement from minus 2 to plus 10 degrees; 24% of hips differed by more than 5 degrees; and of the fourteen hips that were dysplastic by the sourcil, only four were dysplastic by the rim. Radiopaedia states the same 4-degree offset and explains it — the rim includes non-weightbearing bone at the base of the labrum.
An angle is only as good as the two lines it is drawn between. Every threshold on this page assumes the measurement convention stated above, and a different landmark gives a different number from the same hip, heel, knee or spine — not a more or less accurate one. Agreement between observers is part of what a measured angle means, and for several of these angles the published spread between experienced readers is wider than the interval between the thresholds they are read against. Each page here gives the reliability figures with the number of observers and the number of radiographs they came from. This page renders no clinical or surgical decision; it computes the published quantity and states what the literature reports for it, with every threshold and performance figure given with the cohort it came from. A measurement is not a diagnosis, and a figure from a published series is a property of that series rather than a fact about one patient.
Frequently asked questions
What is a normal lateral centre-edge angle?
Hanson and colleagues graded 188 preoperative hips as dysplastic below 20 degrees, borderline dysplastic from 20 to 25 degrees inclusive, normal above 25 and up to 40 degrees, and over-covered above 40 degrees. Radsource states the same boundaries and notes that some surgeons use 18 degrees as the lower figure instead of 20.
Should I measure to the bony rim or to the sourcil?
Say which you used, because the answer changes. Hanson measured the bony-rim angle 4 degrees greater than the sourcil angle on average, with 95% limits of agreement from minus 2 to plus 10 degrees, and of fourteen hips that were dysplastic by the sourcil only four were dysplastic by the rim. Radiopaedia gives the same 4-degree offset and attributes it to the rim including non-weightbearing bone at the labral base.
Why is the horizontal distance on top?
Because the centre-edge angle is measured away from a vertical reference line, so the horizontal offset is the opposite side of the right triangle and the vertical offset the adjacent one. Putting them the other way round returns the complement — a normal 30-degree hip reads 60 degrees — and nothing in the arithmetic objects. The acetabular index and Sharp’s angle are measured from a horizontal reference and so take the vertical distance on top.
How reliable is the measurement?
Very, within one method. Hanson reported inter-observer agreement of 0.92 for the bony-rim angle and 0.92 for the sourcil angle across 188 radiographs. The disagreement is between methods rather than between readers, which is a different and more easily missed problem.
Does this page apply to children?
No. Hanson’s cohort was adults with a mean age of 36.6 years, and the paediatric measure of acetabular development is the acetabular index measured from Hilgenreiner’s line, which has its own page on this site and its own age-dependent normals. One source read for this page reports age-dependent centre-edge-angle normals around 55 years, but its two inequalities point in opposite directions, so nothing from it is used here.
Related calculators
References
- Hanson JA, Kapron AL, Swenson KM, Maak TG, Peters CL, Aoki SK. Discrepancies in measuring acetabular coverage: revisiting the anterior and lateral center edge angles. J Hip Preserv Surg. 2015;2(3):280–286. Preoperative AP radiographs of 188 subjects (109 female, 36.6 ± 11.4 years) who went on to hip arthroscopy for pathomorphology. The classification used here verbatim: lateral coverage was graded “<20° dysplastic, ≥20° and ≤25° borderline dysplastic, >25° and ≤40° normal, and >40° over-covered”. On the two reference points: “On average, the bone LCEA was 4° (95% limits of agreement = −2° to 10°) greater than the sourcil LCEA”, “Forty-six subjects (46/188, 24%) had a LCEA difference greater than 5° between methods”, and of “the 14 subjects with a sourcil LCEA <20° (dysplastic), only four had a bone LCEA also <20°”. “Interobserver agreement was almost perfect for all radiographic measurements: bone LCEA = 0.92, sourcil LCEA = 0.92, bone ACEA = 0.91 and sourcil ACEA = 0.89.”
- Radiopaedia. Lateral centre-edge angle. The construction verbatim: it “is calculated on AP pelvic radiographs by drawing a best fit circle for the inferior and medial margins femoral head”; “The angle is then measured between two lines drawn from the center of the circle, one running vertically along the longitudinal axis of the pelvis and the other to the lateral acetabular rim”. “In a modification by Ogata et al., the second line runs to the lateral edge of the acetabular sourcil”, “which is proposed to be a more functional method given that this measurement includes the weight-bearing portion”. “The lateral acetabular rim method overestimates coverage by ~4° compared to the acetabular sourcil method” “as it includes non-weightbearing bone that forms part of the labral base”. The page gives no diagnostic thresholds at all, which is why the thresholds here come from Hanson et al.
- Stadnick M. Developmental dysplasia of the hip. Radsource MRI Web Clinic, February 2021. “The normal center edge angle is considered to be >25 degrees”; “a center edge angle of less than 20 degrees is consistent with DDH”; “an angle of 20-25 degrees represents borderline dysplasia of the hip (BDH)”, with “a lower range of 18 degrees proposed by some surgeons”. Its vertical reference is NOT the one Radiopaedia gives: the angle is formed by a line perpendicular to the teardrop line drawn through the femoral head centre, and “the lateral-most cortex or lateral sourcil should be indicated as the reference point”. For the acetabular roof obliquity it gives “measurements greater than 10-14 degrees considered to be dysplastic”, and for the femoral head extrusion index “An EI of >27% is defined as dysplastic”.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/