Acetabular Index Calculator (Tonnis Angle)
Acetabular Index Calculator (Tonnis Angle)
The acetabular index from Hilgenreiner’s line, with the two age-band thresholds a source states in text — and a plain statement that this page holds no centile table, because Tonnis’s age norms exist only as a picture.
Acetabular index from Hilgenreiner's line
Arctangent from a horizontal referenceAn AP pelvis in a one-year-old: the superolateral acetabular point sits 9 mm above Hilgenreiner’s line and 24 mm lateral to the triradiate cartilage along it
An arctangent measured from the horizontal
— the angle between Hilgenreiner’s line and a line from the medial acetabular point to the superolateral acetabular rim
- the vertical distance is on TOP here
- because the reference line is HORIZONTAL. That is the reverse of this site’s lateral centre-edge angle page, which is measured from a vertical line and puts the horizontal distance on top. Two angles on one AP pelvis, two orderings; transposing either gives the other’s shape and no error message. The proof for this page asserts the angle rises with the rise and falls with the run, separately, away from the point where the two are equal
- Hilgenreiner’s line
- “drawn through the lower lateral edges of the ilia at the triradiate cartilages”. It is a line through the pelvis and not the edge of the film, so a rotated or tilted radiograph moves it and moves the angle with it
- the lateral point, which Tonnis was specific about
- it “should lie on the sclerotic line of the acetabular roof”, and where the roof is rounded or shows separate anterior and posterior contours because of pelvic position, Tonnis “advised using the true superior rim rather than simply the lowest projected contour”. The lowest projected contour is the easy point to click and the wrong one
- what this page cannot do
- interpolate a centile table. The published age norms are age-, sex- and side-specific means with standard-deviation limits, and this engine has no table interpolation. No curve has been fitted to stand in for them. The two text-stated thresholds — under 30 degrees at birth, under 22 degrees at and beyond one year — are printed instead, with the age band on each
- the adult angle of the same name
- the adult Tonnis angle measures the SLOPE OF THE SOURCIL against a horizontal pelvic reference, not the line to the lateral rim from the triradiate cartilage. Its published thresholds are an order of magnitude lower — dysplastic above 10 to 14 degrees — and reading a paediatric index against them, or the reverse, is the commonest error with this measurement
- derivation
- Hilgenreiner H, 1925, for the reference line; Tonnis D, 1968 and 1976, for the age-related reference ranges. Neither original was reachable and neither is quoted; the landmarks here are LITFL’s rendering of Tonnis and the two thresholds are Radiopaedia’s
Worked example
An AP pelvis in a one-year-old: the superolateral acetabular point sits 9 mm above Hilgenreiner's line and 24 mm lateral to the triradiate cartilage along it
Acetabular index = arctan(9 / 24) = arctan(0.3750) = 20.6 degrees
Radiopaedia's text-stated threshold for this age is that the angle "should measure <22 degrees at and beyond 1 year", so 20.6 sits under it — but read it against the normal for this child's exact age and sex from your own reference source, because this page holds no centile table and the single threshold is a coarse summary of one
Transpose the two distances: arctan(24 / 9) = 69.4 degrees, the complement, which would be a grossly abnormal index in any age band. 20.6 and 69.4 sum to exactly 90, which is the identity the proof uses — and only away from the point where rise equals run, because there both orderings give 45
At birth the same geometry would be read against a different number: "<30 degrees at birth". A newborn index of 27 degrees is under the birth threshold and over the one-year threshold, which is the whole reason the age has to travel with the measurement
Raise the lateral point: 14 mm over the same 24 mm run gives arctan(14 / 24) = 30.3 degrees, above both text-stated thresholds. Lower it to 4 mm and the index is 9.5 degrees, which would be unremarkable in a child and, if it were an adult sourcil slope rather than a paediatric index, would sit right at Radsource's dysplastic boundary of 10 to 14 degrees — the same arithmetic, a different measurement, a different scale
What a source states in TEXT, and what it only pictures
| Source | What its text gives | What is missing |
|---|---|---|
| Radiopaedia, The acetabular angle | “should be <30 degrees at birth”; “should measure <22 degrees at and beyond 1 year” | No values between those two ages, and no sex or side distinction. These are the only paediatric numbers used on this page |
| LITFL, Tonnis angle | The landmarks, in detail, and that Tonnis and Brunken “provided age-, sex- and side-related reference ranges” | Every number. The age-related values exist only inside an image captioned “Age-related acetabular index values, Tonnis 1968”. The body text carries none |
| Wikipedia, X-ray of hip dysplasia | Nothing usable: the sentence reads “In newborns, values of in males and in females are considered normal” | The numbers themselves, absent from the text. A second source that appears to publish the table and does not |
| Radsource, for the ADULT roof obliquity | “measurements greater than 10-14 degrees considered to be dysplastic” | This is a different measurement — the sourcil slope against a horizontal pelvic reference — and its numbers do not transfer to the paediatric index |
Three angles on one AP pelvis, and they are not comparable
| Angle | Reference line | Lateral point | Published figures |
|---|---|---|---|
| Acetabular index (paediatric Tonnis angle) — this page | Hilgenreiner’s line, through the triradiate cartilages | Superolateral acetabular rim, on the sclerotic roof line | Under 30 degrees at birth, under 22 degrees from 1 year (Radiopaedia) |
| Adult Tonnis angle / acetabular roof obliquity | A line parallel to the transverse pelvic axis | The medial and lateral margins of the sourcil, as a tangent | Dysplastic above 10 to 14 degrees (Radsource); 0 to 10 degrees normal (Wikipedia) |
| Sharp’s angle | The line joining the inferior tips of both pelvic teardrops | Lateral edge of the acetabular roof | 33 to 38 degrees usual normal; around 43 degrees and above suspicious (LITFL, reporting Sharp 1961 and Tonnis 1987) |
| Lateral centre-edge angle of Wiberg | A VERTICAL line through the femoral head centre | Lateral acetabular rim, or the sourcil edge in Ogata’s modification | Dysplastic below 20 degrees, normal above 25 and up to 40 (Hanson et al 2015) |
One arctangent, four angles called acetabular, and no table
The acetabular index is the angle between Hilgenreiner’s line — drawn through the lower lateral edges of the ilia at the triradiate cartilages — and a line from the medial acetabular point out to the superolateral acetabular rim. It is the standard radiographic measure of acetabular development in infants and young children. Because the reference line is horizontal, the vertical rise of the lateral point is the numerator here, which is the reverse of the lateral centre-edge angle on this site. Transposing them gives the complement and no error.
Tonnis was specific about the lateral landmark in a way that matters: it should sit on the sclerotic line of the acetabular roof, and where pelvic position produces a rounded or double-contoured roof he advised taking the true superior rim rather than the lowest projected contour. The lowest projected contour is the easier point to click and it gives a different number.
The normal value depends steeply on age, and that is where this page stops short on purpose. Tonnis and Brunken published age-, sex- and side-related reference ranges as centile tables, and this calculator has no table interpolation, so no curve has been fitted to stand in for them: a fitted stand-in misclassifies at the extremes, which is exactly where a hip under surveillance sits. Worse, two independent pages that look as though they publish the table do not. LITFL’s Tonnis angle article carries the age-related values only inside an image; Wikipedia’s hip dysplasia article has lost the numbers out of its own sentence, which reads “In newborns, values of in males and in females are considered normal”. What this page gives instead is the two thresholds a source states in text, each with its age band: under 30 degrees at birth and under 22 degrees at and beyond one year.
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 acetabular index?
It depends on age, and this page does not ask for the age because it holds no centile table. Radiopaedia’s acetabular angle article gives the only two age-band thresholds any source read for this page states in text: the index should be under 30 degrees at birth and under 22 degrees at and beyond one year. Take the normal for the patient’s own age and sex from your own reference source.
Why does this calculator not use Tonnis’s age tables?
Two reasons. The engine behind this site has no table interpolation, and a fitted curve standing in for a published centile table misclassifies at the extremes, which is where the clinical question sits. And the tables could not be read: LITFL’s Tonnis angle page carries them only inside an image, and Wikipedia’s version has the numbers missing from its sentence altogether.
Is the acetabular index the same as the Tonnis angle?
In infants and young children, yes — LITFL states that “Tonnis angle is the acetabular roof angle (acetabular index) measured on an AP pelvic radiograph in infants and young children”. In adults the name is used for a different measurement, the slope of the sourcil against a horizontal pelvic reference, whose published thresholds are around 10 to 14 degrees rather than 22 to 30. The two are not interchangeable.
Which lateral point should I use?
Tonnis specified the point on the sclerotic line of the acetabular roof, and where the roof is rounded or shows separate anterior and posterior contours because of pelvic position, the true superior rim rather than the lowest projected contour. The lowest projected contour gives a different, smaller angle.
Why is the vertical distance the numerator here but not on the centre-edge angle page?
Because the reference lines differ. The acetabular index is measured away from a horizontal line, Hilgenreiner’s, so the vertical rise is the opposite side of the right triangle. The lateral centre-edge angle is measured away from a vertical line, so there the horizontal offset is on top. Swapping either pair returns the complement of the right answer, which is a plausible number rather than an error.
Related calculators
References
- Radiopaedia. The acetabular angle (article 6298). The paediatric construction verbatim: “the angle is formed by a horizontal plane of the pelvis” defined by “a line connecting both triradiate cartilages (Hilgenreiner line)” and “a second line that extends through to the lateral aspect of the acetabular roof”. The two age-band thresholds, which are the only ones any source read for this page states in text: it “should be <30º at birth” and “should measure <22º at and beyond 1 year”. For adults the same page states that “the horizontal plane of the pelvis defined as the inferior margin of the pelvic teardrop is used instead”, with a normal range of “33º to 38º”, an increased angle “reported at >42º” or “≥45º” and a decreased angle “<32º” — which is Sharp’s angle, and is why this site carries it as a separate page.
- Life in the Fast Lane (LITFL). Tönnis angle. “Tönnis angle is the acetabular roof angle (acetabular index) measured on an AP pelvic radiograph in infants and young children.” “Hilgenreiner line is drawn through the lower lateral edges of the ilia at the triradiate cartilages”; “From this medial acetabular point, a second line is drawn along the sclerotic acetabular roof to the superior lateral acetabular rim”; “The angle between the two is the acetabular index (AC angle).” On the landmark that decides the number: “Tönnis specified that the lateral point should lie on the sclerotic line of the acetabular roof”, and where the roof is rounded or double-contoured by pelvic position “Tönnis advised using the true superior rim rather than simply the lowest projected contour”. The page’s age-related reference values are not in its text. They exist only inside an image captioned “Age-related acetabular index values, Tönnis 1968”, and the body says only that Tönnis and Brunken “provided age-, sex- and side-related reference ranges”. Nothing from that image is used here.
- Stadnick M. Developmental dysplasia of the hip. Radsource MRI Web Clinic, February 2021. For the adult acetabular roof obliquity — which this source lists as the same measure as the Tönnis angle and the acetabular index, measured between “a line parallel to the transverse pelvic axis” and a line tangential to the medial and lateral margins of the sourcil — “measurements greater than 10-14 degrees considered to be dysplastic”. The number is different from the paediatric thresholds above because the reference line and the lateral landmark are both different, which is the point this page makes.
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/