Bohler Angle Calculator (Calcaneus)
Bohler Angle Calculator (Calcaneus)
Bohler’s tuber joint angle from the two drops it is built out of, with the three published normal ranges that disagree about where it starts — and the 76-degree spread between experienced readers measuring the same fractured heel.
Bohler's tuber joint angle from two line inclinations
Two arctangents about the posterior facetA lateral foot radiograph: the posterior facet apex sits 9 mm above the calcaneal tuberosity and 30 mm in front of it, and 12 mm above the anterior process and 38 mm behind it
Two inclinations about one apex
— the two lines cross at the posterior facet, and the angle between them is the sum of the angles each makes with the horizontal
- why a sum and not a difference
- both lines descend from the posterior facet, one backwards to the tuberosity and one forwards to the anterior process. Extended through the apex they cross at an angle equal to the sum of their two inclinations. A perfectly flat calcaneus gives two zero inclinations and an angle of zero, which is exactly what a depressed intra-articular fracture is described as doing, and a facet dropped below the line joining the other two points gives negative inclinations and a negative angle. Signed drops therefore carry the whole clinical range with no special case
- transposing a drop and its run gives the complement
- arctan(30/40) is 36.87 degrees and arctan(40/30) is 53.13 — the complement, not an error, and both land inside the plausible range for this angle. The proof for this page asserts that each inclination RISES with its drop and FALLS with its run, separately, at three base points chosen away from drop equal to run, where every transposed version agrees and the test proves nothing
- if your workstation gives you the angles
- use them. The quantity is the sum of the two line inclinations; the four distances here exist because a reader working from a plain film with a ruler has drops and runs rather than angles, not because the distances are the definition
- the landmark that moves the answer
- the apex is the highest point of the POSTERIOR ARTICULAR FACET, not the highest point of the sclerotic line and not the midpoint of the calcaneus. EBM Consult records that some sources place the middle point at the calcaneal midpoint and describe the third point as the lowest rather than the highest, and a page quoting a normal range has to say which landmarks that range was measured with
- derivation
- Bohler L, J Bone Joint Surg 1931. The citation was read in the reference lists of the sources below; the 1931 paper itself was not reachable, so the landmarks here are quoted from Radiopaedia and EBM Consult and the normal ranges from those two plus a 130-radiograph normal series
Worked example
A lateral foot radiograph: the posterior facet apex sits 9 mm above the calcaneal tuberosity and 30 mm in front of it, and 12 mm above the anterior process and 38 mm behind it
Posterior inclination = arctan(9 / 30) = arctan(0.3000) = 16.70 degrees
Anterior inclination = arctan(12 / 38) = arctan(0.3158) = 17.50 degrees
Bohler's angle = 16.70 + 17.50 = 34.2 degrees, inside both published normal ranges and within one standard deviation of the 34 plus or minus 5 degree mean Simunovic measured in 130 normal adult radiographs
Now transpose the posterior pair: arctan(30 / 9) = 73.30 degrees, and the total becomes 90.8 degrees. That one is obvious. Transpose a pair that is closer together — make the anterior drop 20 mm over a run of 25 mm and the inclination is 38.66 degrees, against 51.34 degrees transposed, giving totals of 55.4 and 68.0 degrees. Neither is an error and neither throws; this is why the direction of each argument is asserted separately
Flatten the heel: with the facet only 1 mm above the tuberosity and 1 mm above the anterior process the angle falls to 3.4 degrees, and with the facet 4 mm BELOW both it becomes negative — the published behaviour of a depressed intra-articular fracture, and the reason this page accepts signed drops
The same heel on a film shot 25 degrees cephalad could read 11 degrees differently, per the Harvard cadaver series. A Bohler angle is a property of the projection as much as of the bone
Three published normal ranges, and they do not agree
| Source | Normal range | What else it states |
|---|---|---|
| Radiopaedia, Bohler angle | 25 to 40 degrees | No numeric abnormal threshold at all. “A mildly decreased Bohler angle may be seen in a normal individual” |
| EBM Consult | 20 to 40 degrees | “Angles < 20 degrees is suggestive of a calcaneus fracture and/or disruption of the posterior facet”. Also notes that sources disagree about where the landmark points sit |
| Simunovic et al, Foot Ankle Surg 2018; 130 adult radiographs, three raters | Mean 34 plus or minus 5 degrees, observed range 21 to 46 | Not related to age, sex or side. Interrater ICC 0.94. The abstract calls 21 to 46 the observed range, not a derived reference interval |
| Touissaint et al, Orthop J Harvard Med Sch 2013, citing earlier series | “Widely accepted” 25 to 40 degrees | Records population variation “between 14 degrees in Malawians and up to 50 degrees in Ugandan subjects” |
How well two readers agree, and on which feet
| Study | Cohort | Agreement |
|---|---|---|
| Simunovic et al 2018 | 130 lateral radiographs of UNINJURED adult feet, three raters | “The interrater reliability was almost perfect (ICC=0.94)” |
| Touissaint et al 2013 | One cadaver, 41 observers, true lateral image | “The interobserver correlation was excellent, ICC = 0.985” |
| Otero et al, Foot Ankle Surg 2015 | 34 pre- and post-operative radiographs of DISPLACED INTRA-ARTICULAR calcaneal fractures, four orthopaedic surgeons | Inter-observer ICC 0.83 then 0.77; intra-observer 0.83 to 0.98. “With an allowed discrepancy of 20 degrees, there was lack of consensus for BA in 37.5%” of measurements, and “The 95% confidence interval for 90% agreement in BA involved a range of 76 degrees” |
| Otero et al 2015, the crucial angle of Gissane for comparison | The same 34 radiographs | Inter-observer ICC “0.28 and 0.1 in the two sessions”, intra-observer 0.16 to 0.67 — which is why this page computes Bohler’s angle and not that one |
One angle, three normal ranges, and a 76-degree spread
Bohler’s angle, the tuber joint angle, is the angle at which two lines cross on a lateral foot radiograph: one drawn from the highest point of the calcaneal tuberosity to the highest point of the posterior articular facet, the other from that facet to the highest point of the anterior process. Because both lines descend from the facet, the angle between them is simply the sum of the two inclinations, which is what this page adds up. A flat calcaneus gives zero; a facet driven below the line joining the other two points gives a negative angle, which is why the inputs here are signed.
The normal range is where the sources part company. Radiopaedia gives 25 to 40 degrees, EBM Consult 20 to 40, and a 2018 series of 130 uninjured adult Croatian feet measured a mean of 34 plus or minus 5 degrees with an observed range of 21 to 46. A heel measuring 22 degrees is therefore abnormal on one published range, normal on another, and ordinary among 130 normal feet. The Harvard group’s review adds the population dimension, citing reported values from 14 degrees in Malawian subjects to 50 degrees in Ugandan ones. This page prints all of them and bands the overlap rather than picking a winner.
The second problem is bigger than the first. Otero and colleagues gave 34 radiographs of displaced intra-articular calcaneal fractures to four orthopaedic surgeons: inter-observer agreement was 0.83 and then 0.77, which sounds respectable, but the interval containing 90% of reader-to-reader differences spanned 76 degrees, and even allowing a 20-degree discrepancy the four readers failed to agree on 37.5% of measurements. Agreement on uninjured feet is a different matter entirely — 0.94 across 130 radiographs, 0.985 across 41 observers reading one cadaver — so the reliability of this angle collapses precisely on the films it is used for.
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 Bohler’s angle?
It depends which source you use. Radiopaedia gives 25 to 40 degrees and EBM Consult 20 to 40, while a 2018 series of 130 uninjured adult feet measured a mean of 34 plus or minus 5 degrees with an observed range of 21 to 46. All three are printed on this page. A value between 20 and 25 degrees is normal on one published range and not on another.
How is Bohler’s angle measured?
On a lateral foot radiograph, between a line joining the highest point of the calcaneal tuberosity to the highest point of the posterior articular facet, and a line joining that facet to the highest point of the anterior process. This page takes the vertical drop and horizontal run of each line from the facet and adds the two inclinations, which is the same angle.
Can Bohler’s angle be zero or negative?
Yes, and that is a real finding rather than an input error. The angle falls as the posterior facet is depressed towards the line joining the tuberosity and the anterior process, reaches zero when all three points are collinear, and goes negative when the facet drops below that line. This calculator accepts negative drops for exactly that reason.
Why does the same heel measure differently on two films?
Because the measurement depends on the projection. A cadaver study at Harvard found the angle changed by up to 6 degrees with the x-ray beam angled 15 degrees cephalad and by 11 degrees at 25 degrees cephalad, while a posteriorly directed oblique changed it by only about 2 degrees. The authors recommended avoiding cephalad oblique laterals.
How much do two experienced readers agree?
It depends entirely on the foot. On 130 uninjured adult radiographs the interrater intraclass correlation was 0.94. On 34 radiographs of displaced intra-articular calcaneal fractures read by four orthopaedic surgeons it was 0.83 and then 0.77, but the interval containing 90% of differences between readers spanned 76 degrees and the surgeons disagreed by more than 20 degrees on 37.5% of measurements.
Does this page compute the crucial angle of Gissane?
No. In the same study that measured Bohler’s angle on 34 fracture radiographs, inter-observer agreement for the crucial angle of Gissane was 0.28 and then 0.1, with intra-observer values from 0.16 to 0.67. A measurement two experienced readers cannot reproduce is not worth a calculator.
Related calculators
References
- Radiopaedia. Böhler angle. The two lines verbatim: “the angle on a lateral foot radiograph between a line joining the highest point of the anterior process of the calcaneus and the highest point of the posterior articular facet, and a line joining the highest point of the posterior articular facet with the highest point of the calcaneal tuberosity”. “The normal value for the Böhler angle is between 25° and 40°.” Also: “A reduced Böhler angle can be seen in displaced intra-articular calcaneal fractures” and “A mildly decreased Böhler angle may be seen in a normal individual”. The page states no numeric threshold for abnormality and does not mention the angle of Gissane.
- EBM Consult. Böhler’s angle and calcaneus fractures. Gives the three points explicitly, the first line running to “point 2 (the most cephalic or highest point of the posterior facet)” and the second from point 2 “to point 3 (the highest point of the calcaneus bone that forms the articular surface for the cuboid bone)”. Its normal range DISAGREES with Radiopaedia’s: “The normal range is 20 to 40 degrees”, with “Angles < 20 degrees is suggestive of a calcaneus fracture and/or disruption of the posterior facet”. It also notes that sources differ on where the landmark points sit, which is why both ranges are printed on this page rather than reconciled.
- Šimunović M, Nizić D, Pervan M, Radoš M, Jelić M, Kovačević B. The physiological range of the Böhler’s angle in the adult Croatian population. Foot Ankle Surg. 2018;25(2):174–179. Three raters measured 130 digital lateral foot radiographs in PACS, selected from 248 after exclusions. “The mean value of the Böhler’s angle was 34±5° (21-46°).” It was not related to age (p=0.057), sex (p=0.344) or laterality (p=0.618). “The interrater reliability was almost perfect (ICC=0.94).” The 21 to 46 degree figure is the observed range in this sample and the abstract does not call it a derived reference interval.
- Otero JE, Westerlind BO, Tantavisut S, Karam MD, Phisitkul P, Akoh CC, Gao Y, Marsh JL. There is poor reliability of Böhler’s angle and the crucial angle of Gissane in assessing displaced intra-articular calcaneal fractures. Foot Ankle Surg. 2015;21(4):277–281. Thirty-four pre- and post-operative lateral radiographs of displaced intra-articular calcaneal fractures, read by four orthopaedic surgeons. Inter-observer ICC for the Böhler angle “0.83 in the first session and 0.77 in the second”; intra-observer “ranged from 0.83 to 0.98”. For the crucial angle of Gissane, inter-observer ICC “0.28 and 0.1”. “With an allowed discrepancy of 20°, there was lack of consensus for BA in 37.5%”, and “The 95% confidence interval for 90% agreement in BA involved a range of 76°.” The authors “recommend use of caution when applying BA as currently measured in making treatment decisions”.
- Touissaint RJ, Gitajn L, Kwon J. Measuring Bohler’s angle with oblique lateral radiographs: implications for management of calcaneal fractures. The Orthopaedic Journal at Harvard Medical School. 2013;15. One fresh-frozen cadaver imaged in 5° increments from 0 to 25° in four directions, read by 41 observers (five attendings, 36 residents). “The true Bohler’s angle measured on the perfect lateral image was determined to be 35 degrees”; “The interobserver correlation was excellent, ICC = 0.985”. On obliquity: the angle varies “up to 6 degrees when the x-ray beam is directed 15 degrees cephalad”, “increased to 11 degrees” at 25° cephalad, and “only a two-degree change with 25-degree oblique laterals” posteriorly; “Oblique lateral radiographs in the cephalad direction should be avoided.” It records population variation as “a range of values between 14 degrees in Malawians and up to 50 degrees in Ugandan subjects”, and calls 25 to 40 degrees “widely accepted”. The standard deviations in its Table 1 are an image and are not quoted.
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/