Sharp Angle Calculator (Acetabular Inclination)
Sharp Angle Calculator (Acetabular Inclination)
Sharp’s angle from the inter-teardrop line, with his own 1961 bands in 200 hips — and the three different upper limits that four sources put at 42, 43, 45 and 47 degrees.
Sharp's acetabular inclination angle
Arctangent from the inter-teardrop lineAn AP pelvis: the lateral edge of the acetabular roof sits 29 mm above the inter-teardrop line and 42 mm lateral to the teardrop tip along it
An arctangent from the inter-teardrop line
— the angle between the line joining the inferior tips of both pelvic teardrops and a line from that tip to the lateral edge of the acetabular roof
- the rise is on TOP
- because the reference line is horizontal, as it is for the acetabular index and unlike the lateral centre-edge angle, which is measured from a vertical line and puts the horizontal offset on top. Transposing the pair gives the complement: a normal 35-degree hip reads 55 degrees transposed, a plausible-looking number for a dysplastic one. The proof asserts the angle rises with the rise and falls with the run, separately, away from the point where they are equal
- the teardrop is the landmark that defines the method
- “The Sharp angle is measured from the inferior tip of the pelvic teardrop (U-figure)”, with “the line joining the two U-figures providing the horizontal reference”. Using the acetabular notch instead, as Ullmann did in 1938, is a different measurement with a different upper limit; the two are often quoted together as the Ullmann-Sharp angle, and Stulberg and Harris’s normal series is reported under that joint name
- both hips at once, and that is the point
- the reference line is built from both teardrops, so the same line serves both sides and the contralateral hip is measured against the identical horizontal. That makes the side-to-side difference on one film the most robust thing this measurement produces
- four published upper limits, in one hip
- 42 degrees (Radiopaedia’s first cited threshold, and the top of Sharp’s upper-normal band), 43 degrees (Tonnis 1987, suspicious in adolescents and adults), 45 degrees (Ullmann 1938, and Radiopaedia’s second cited threshold, and Wikipedia’s table) and 47 degrees (the top of Sharp’s uncertain band). All four are printed on this page and none is corrected
- derivation and its cohort
- Sharp IK, J Bone Joint Surg Br 1961, reported by LITFL as a series of 200 hips in 100 adults over 60 years of age — an elderly cohort, which is worth knowing before applying his bands to a 25-year-old. Sharp’s paper was not reachable; every figure attributed to it here was read in LITFL’s account of it
Worked example
An AP pelvis: the lateral edge of the acetabular roof sits 29 mm above the inter-teardrop line and 42 mm lateral to the teardrop tip along it
Sharp's angle = arctan(29 / 42) = arctan(0.6905) = 34.6 degrees, inside the 33 to 38 degree usual normal range reported from Sharp's own 200 hips and stated independently by Radiopaedia
Transpose the two distances: arctan(42 / 29) = 55.4 degrees, the complement, which would be above every published limit. The two sum to exactly 90, which is the identity the proof uses — and only away from rise equal to run, where both orderings give 45 and the test is empty
Raise the roof edge to 36 mm over the same run: arctan(36 / 42) = 40.6 degrees. That is the upper end of normal on Sharp's bands as LITFL reports them (39 to 42 degrees), plainly normal on Radiopaedia's increased-above-42 threshold, and inside Stulberg and Harris's normal series, which extended to about 41 degrees
At 40 mm: arctan(40 / 42) = 43.6 degrees. Now the sources split — suspicious for dysplasia on Tonnis's figure of about 43 degrees or greater, inside the limit on Ullmann's 45 degrees, and of uncertain significance on Sharp's own 42 to 47 band. Same hip, three published answers, which is why all three are on the page
Flatten it instead: 24 mm over 42 mm gives arctan(24 / 42) = 29.7 degrees, under Radiopaedia's decreased threshold of 32 degrees. A flat roof is the opposite deformity and not a better one
Sharp’s own bands, and three other published limits
| Band or limit | Figure | Source, as read |
|---|---|---|
| Usual normal range | 33 to 38 degrees | Sharp 1961, 200 hips in 100 adults over 60, as reported by LITFL. Radiopaedia states the same range independently for adults |
| Upper end of normal | 39 to 42 degrees | Sharp 1961 via LITFL, which also illustrates a 42-degree hip as morphologically normal |
| Significance uncertain | 42 to 47 degrees | Sharp 1961 via LITFL. His bands OVERLAP at 42 degrees and the source does not resolve the boundary |
| Suspicious for dysplasia | Around 43 degrees or greater | Tonnis 1987, in adolescents and adults, via LITFL |
| Upper limit in younger subjects | About 45 degrees | Ullmann 1938 via LITFL — measured from the acetabular notch rather than the teardrop tip. Radiopaedia also cites 45 degrees or more as increased, and Wikipedia’s table gives under 45 degrees as normal |
| Decreased | Below 32 degrees | Radiopaedia, The acetabular angle |
| Normal mean | Around 33 to 35 degrees, ranging to about 41 | Stulberg and Harris 1974 normal series, reported under the Ullmann-Sharp name, via LITFL |
Why this is a separate page from the acetabular index
| Sharp’s angle | Acetabular index | |
|---|---|---|
| Reference line | The line joining the inferior tips of both pelvic teardrops | Hilgenreiner’s line, through the lower lateral edges of the ilia at the triradiate cartilages |
| Medial point | The inferior tip of the teardrop | The lower lateral edge of the ilium at the triradiate cartilage |
| Population | Adults and adolescents | Infants and young children, before the triradiate cartilage closes |
| Usual normal | 33 to 38 degrees | Under 30 degrees at birth, under 22 degrees from one year |
| Same arithmetic? | Yes — both are arctan(rise / run) from a horizontal reference | Yes, and that is exactly why the two numbers get read against each other’s thresholds |
The inter-teardrop line, and four answers to one question
Sharp’s angle measures acetabular inclination in the adult hip. The horizontal reference is the line joining the inferior tips of both pelvic teardrops; the second line runs from that tip on the side being measured out to the lateral edge of the acetabular roof, and the angle between them is the measurement. Because the reference is horizontal, the vertical rise of the roof edge is the numerator here — the same ordering as the acetabular index and the reverse of Wiberg’s centre-edge angle.
The reference line is the reason this measurement is worth having. It is built from both teardrops, so both hips are measured against exactly the same horizontal on one film, and the side-to-side difference is the most robust thing the method produces. It is also its weakness: the teardrops are pelvic landmarks, so pelvic rotation or tilt moves the reference and the angle follows.
The thresholds are a genuine mess and the page prints the mess. LITFL reports Sharp’s own 1961 series of 200 hips in 100 adults over 60 as giving 33 to 38 degrees as the usual normal range, 39 to 42 as the upper end of normal and 42 to 47 as a band whose significance is uncertain, with 47 degrees illustrated as congenital subluxation — and his two upper bands overlap at 42 degrees, which the source does not resolve. Radiopaedia gives 33 to 38 degrees as normal with increased values “reported at above 42” or “45 or more”. Tonnis in 1987 regarded around 43 degrees or more as suspicious in adolescents and adults. Ullmann in 1938, measuring from the acetabular notch rather than the teardrop, put the upper limit at about 45 degrees in younger subjects. A hip at 44 degrees is therefore suspicious, within limits, or of uncertain significance depending on which paper you have in front of you.
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 Sharp angle?
LITFL reports Sharp’s own 1961 series of 200 hips in 100 adults over 60 as giving 33 to 38 degrees as the usual normal range, and Radiopaedia states the same range for adults. Values from 39 to 42 degrees are the upper end of normal on Sharp’s stratification, and Stulberg and Harris’s normal series extended to about 41 degrees.
At what angle is the acetabulum called dysplastic?
The sources disagree, and all of their figures are on this page. Sharp left 42 to 47 degrees as uncertain in meaning; Tonnis in 1987 regarded around 43 degrees or greater as suspicious in adolescents and adults; Ullmann in 1938 put the upper limit at about 45 degrees in younger subjects, which is also Radiopaedia’s second cited threshold and Wikipedia’s table value; and Radiopaedia’s first cited increased threshold is above 42 degrees.
Is Sharp’s angle the same as the acetabular index?
The arithmetic is identical and the measurement is not. Sharp’s angle uses the line joining the inferior tips of both pelvic teardrops as its horizontal and is an adult measurement; the acetabular index uses Hilgenreiner’s line through the triradiate cartilages and is a paediatric one. Their normal ranges differ by more than ten degrees, so reading one against the other’s thresholds is a real error.
Does pelvic rotation change the angle?
Yes. The reference line is drawn through a pelvic landmark rather than the edge of the film, so rotation or tilt moves it and the measured angle with it. Because the same line serves both hips, the difference between the two sides on one radiograph is less affected than either absolute value.
Which medial point should I use?
For Sharp’s angle, the inferior tip of the pelvic teardrop, the U-figure, with the line joining both teardrops as the horizontal reference. Ullmann’s earlier version used the lowest point of the acetabular teardrop or the acetabular notch and ran to the superior acetabular rim, which is a different measurement with its own published limit.
Related calculators
References
- Life in the Fast Lane (LITFL). Sharp angle. “The Sharp angle is measured from the inferior tip of the pelvic teardrop (U-figure).” “A horizontal reference is drawn through the corresponding points of both teardrops,” and “a second line extends from the inferior teardrop to the lateral edge of the acetabular roof.” “The angle between these lines represents acetabular inclination.” On Sharp’s own 1961 series of 200 hips in 100 adults over 60, as this page reports it: 33–38 degrees is the usual normal range, 39–42 degrees the upper end of normal, and 42–47 degrees a band whose significance is uncertain, with 47 degrees given as an example of congenital subluxation. The page also records Ullmann (1938) measuring from “the lowest point of the acetabular teardrop or acetabular notch” — a different landmark — with about 45 degrees as the upper limit in younger subjects; Stulberg and Harris (1974), whose “normal series gave mean Ullmann–Sharp values around 33–35°, with ranges extending to approximately 41°”; and Tönnis (1987), who “regarded values around 43° or greater as suspicious for dysplasia in adolescents and adults”. Sharp’s bands overlap at 42 degrees and the page does not resolve the boundary.
- Radiopaedia. The acetabular angle (article 6298). For adults, “the horizontal plane of the pelvis defined as the inferior margin of the pelvic teardrop is used instead” of Hilgenreiner’s line. “The normal range is 33º to 38º”; an increased angle is “reported at >42º” or “≥45º”; “A decreased acetabular angle is <32º”. The two reported upper limits, 42 and 45 degrees, are cited to different references on the same page and are both printed here.
- Wikipedia. X-ray of hip dysplasia. Its adult hip table gives Sharp’s angle as “<45° Greater indicates acetabular dysplasia” and the adult Tönnis angle as “0 to 10° >10° is a risk factor for instability”, both unattributed to a specific paper. Its centre-edge angle row reads “>20° (<55 years old); <24° (>55 years old); >40° indicates overcoverage”, in which the second inequality points the wrong way; that row is internally inconsistent and nothing from it is used anywhere on this site. Its acetabular index sentence reads “In newborns, values of in males and in females are considered normal” — the numbers are absent from the text, a second source that appears to publish the paediatric table and does not.
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/