Posterior Tibial Slope Calculator
Posterior Tibial Slope Calculator
Posterior tibial slope by Bernhardson’s published method — 90 degrees minus the plateau-to-axis angle — for the medial and lateral plateaus separately, with the cohort means and the 12-degree figure two sources give.
Posterior tibial slope, medial and lateral
90 degrees minus the measured plateau angleA lateral knee radiograph with the proximal tibial anatomical axis drawn from the 5 cm and 15 cm cortical midpoints: the medial plateau tangent meets that axis at 81.5 degrees and the lateral plateau tangent at 79 degrees
A subtraction from ninety
— measured separately for the medial and the lateral plateau
- why there is no arctangent here
- because the measured quantity is already an angle. Bernhardson’s published method marks points on the cortices, builds the axis, measures the angle between the plateau tangent and that axis, and ends “the resultant angle was subtracted from 90 to determine the posterior tibial slope angle”. The subtraction IS the formula. A rise-and-run version would have to be measured against the film horizontal instead of the tibial axis, and that is a different quantity
- the axis is the measurement
- “points 5 and 15 cm distal to the joint line on the anterior and posterior tibial cortices”, each pair joined, and the axis drawn “to intersect through both midpoints”. A slope measured against the posterior cortex, or against the film edge, is not this number. Radiopaedia’s own description — two lines tangential to the posterior tibial cortex and the tibial plateau, with the angle between them taken as the slope — read literally returns an angle near 90 degrees rather than near 8, which is why this page follows Bernhardson
- direction, and what a negative answer means
- the slope FALLS as the measured plateau-to-axis angle rises, by one degree per degree. Above 90 degrees the slope is negative, which means the plateau tilts anteriorly rather than posteriorly. The proof asserts that monotonic decrease at three base points and the exact unit slope of the relation
- medial and lateral are different numbers
- Radiopaedia gives means of about 7.7 degrees medially and 6.85 degrees laterally. The anterior cruciate literature generally works with the lateral slope, which is why it is a separate figure here rather than folded into an average. A paper’s threshold applies to the plateau that paper measured
- radiograph or MRI
- not interchangeable. Bernhardson measured on lateral radiographs; the series in Di Benedetto’s review measured on sagittal MRI by Hudek’s method, against “the line orthogonal to the longitudinal tibial axis of the MRI”, and its mean lateral slope of 10.9 degrees is higher than Bernhardson’s radiographic control mean of 8.6. Say which modality a slope came from
- reliability
- Bernhardson reported an inter-rater intraclass correlation of 0.852 and an intra-rater value of 0.872, with two raters measuring and a third measuring a random sample of 65 patients. Good, but against bands a few degrees wide
Worked example
A lateral knee radiograph with the proximal tibial anatomical axis drawn from the 5 cm and 15 cm cortical midpoints: the medial plateau tangent meets that axis at 81.5 degrees and the lateral plateau tangent at 79 degrees
Medial posterior tibial slope = 90 − 81.5 = 8.5 degrees, close to Bernhardson's control mean of 8.6 plus or minus 2.2 degrees in 104 matched patients and to Radiopaedia's medial mean of about 7.7 degrees
Lateral posterior tibial slope = 90 − 79 = 11.0 degrees. The two plateaus differ on the same knee, which is why both are printed; Radiopaedia's lateral mean is about 6.85 degrees
The relation is exactly one degree per degree, and it runs the wrong way round. Increase the measured plateau-to-axis angle to 84 degrees and the slope FALLS to 6.0 degrees; drop it to 78 and the slope RISES to 12.0. A reader who subtracts 90 from the measured angle instead of subtracting the measured angle from 90 gets the negative of the right answer, which is why the direction is asserted separately in this page's proof
Land on both boundaries. A measured angle of exactly 84 degrees gives 6.0 degrees of slope, the figure Bernhardson associates with increased force on the posterior cruciate; exactly 78 degrees gives 12.0, the figure two sources attach to increased risk after anterior cruciate reconstruction. This page reads 12.0 as the top of the middle band, because both sources state their threshold as greater than, or as 12 or more
A plateau tilting the other way: a measured angle of 94 degrees gives −4.0 degrees, an anterior slope. The calculation handles it, and the published associations above do not extend there
What the slope measures in named cohorts
| Group | Slope | Cohort and modality |
|---|---|---|
| Posterior cruciate ligament injury | 5.7 plus or minus 2.1 degrees | 104 patients, lateral radiographs, Bernhardson et al, Am J Sports Med 2019 |
| Matched controls | 8.6 plus or minus 2.2 degrees | 104 matched patients, same study and modality |
| Population means by plateau | About 7.7 degrees medially, 6.85 degrees laterally | Radiopaedia; means rather than a reference range |
| Anterior cruciate graft failure, lateral slope | 8.4 degrees against 6.5 degrees in comparators | Christensen et al, as reported in Di Benedetto’s review; sagittal MRI |
| A surgical series’ own lateral slope | 10.9 degrees on average; 11.8 in women against 8.7 degrees in men | 36 patients, 26 female, sagittal T1 MRI by Hudek’s method, Di Benedetto et al, Acta Biomed 2020 |
The two thresholds, and what each is attached to
| Figure | What the source states | Source |
|---|---|---|
| Less than about 6 degrees | “a flattened tibial slope of approximately < 6 degrees may increase the force on the PCL” | Bernhardson et al 2019, from a case-control comparison of 104 and 104 |
| 12 degrees or more | “Increased (up to 5x) risk of further injury after ACL reconstruction with a posterior tibial slope of 12 degrees or more” | Radiopaedia |
| Greater than 12 degrees | “an incidence close to 60% for graft rupture or contralateral ACL injury” | Webb et al, as reported in Di Benedetto’s review. Webb’s cohort size is not stated there and is not given here |
| Per 2, 4 and 6 degrees | Relative risk of graft failure “of 1.6 with a 2 degree slope increase”, “2.4 with a 4 degree increase, and 3.8 with a 6 degree slope increase” | Christensen et al, as reported in the same review — a continuous relation rather than a threshold |
| Reliability of the measurement | Inter-rater intraclass correlation 0.852, intra-rater 0.872 | Bernhardson et al 2019; two raters, with a third measuring a random sample of 65 |
Ninety minus the measured angle, and which plateau
The posterior tibial slope is the posterior inclination of the tibial plateau relative to the proximal tibial anatomical axis. Bernhardson and colleagues set out the method explicitly: mark points 5 and 15 cm distal to the joint line on the anterior and posterior tibial cortices, join each pair, draw the axis through both midpoints, measure the angle between the plateau tangent and that axis, and subtract the result from 90. That last step is this page’s arithmetic. There is no arctangent here because the measured quantity is already an angle, and asking a reader for a rise and a run would produce a slope against the film horizontal instead of against the tibial axis — a different number.
The axis is the measurement, and the sources do not all describe it the same way. Radiopaedia’s page describes two lines tangential to the posterior tibial cortex and the tibial plateau with the angle between them taken as the slope; read literally that construction returns an angle near 90 degrees rather than near 8, and its reference is the posterior cortex rather than the anatomical axis. This page follows Bernhardson’s stated method and prints Radiopaedia’s population means beside it.
Medial and lateral are different numbers on the same knee — about 7.7 degrees medially against 6.85 laterally on Radiopaedia’s means — and the anterior cruciate literature generally works with the lateral slope. Both are therefore computed here rather than averaged. Modality matters as much: Bernhardson measured on lateral radiographs, while the series in Di Benedetto’s review measured on sagittal MRI by Hudek’s method and reported a mean lateral slope of 10.9 degrees, higher than Bernhardson’s radiographic control mean of 8.6. A threshold travels with the modality and the plateau it was derived on.
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 posterior tibial slope?
Radiopaedia gives means of about 7.7 degrees for the medial plateau and 6.85 degrees for the lateral, which are means rather than a reference range. Bernhardson’s 104 matched control patients averaged 8.6 plus or minus 2.2 degrees on lateral radiographs. The medial and lateral slopes differ on the same knee.
Why is the formula 90 minus the measured angle?
Because the slope is defined against a line perpendicular to the proximal tibial anatomical axis, while what a protractor measures is the angle to the axis itself. Bernhardson’s published method ends with exactly this step: the resultant angle was subtracted from 90 to determine the posterior tibial slope angle. Subtracting 90 from the measured angle instead gives the negative of the right answer.
Which plateau should I measure?
Both, and say which when you quote a number. This page computes the medial slope as the headline and the lateral slope underneath it. The anterior cruciate literature generally works with the lateral slope — Di Benedetto’s review measures the lateral plateau specifically — and the published means for the two differ by about a degree.
What slope is associated with anterior cruciate graft failure?
Two sources put a figure at 12 degrees. Radiopaedia reports an increased risk, up to fivefold, of further injury after reconstruction at 12 degrees or more, and Di Benedetto’s review reports Webb finding close to a 60% incidence of graft rupture or contralateral injury above 12 degrees, without stating Webb’s cohort size. The same review reports Christensen’s continuous estimate: relative risk 1.6 per 2 degrees of extra slope, 2.4 per 4 and 3.8 per 6.
Can the slope be negative?
Yes. If the measured angle between the plateau tangent and the tibial axis is greater than 90 degrees, the plateau tilts anteriorly and the slope is negative. The calculation handles it; the published associations above were derived in knees with posterior slopes and do not extend there.
Related calculators
References
- Bernhardson AS, DePhillipo NN, Daney BT, Kennedy MI, Aman ZS, LaPrade RF. Posterior tibial slope and risk of posterior cruciate ligament injury. Am J Sports Med. 2019;47(2):312–317, read in the authors’ institutional open-access copy. The method verbatim: “Posterior tibial slope was measured by first marking points 5 and 15 cm distal to the joint line on the anterior and posterior tibial cortices”; “A line was drawn to connect the two points marked at 5 cm, and again for the two points marked at 15 cm”; “the tibial proximal anatomical axis was drawn to intersect through both midpoints”; the quantity is the angle between “the posterior inclination of the medial and lateral tibial plateaus, and the perpendicular line” drawn “with respect to the tibial proximal anatomical axis”; and, in the Figure 2 caption, “Lastly, the resultant angle was subtracted from 90 to determine the posterior tibial slope angle” — which is this page’s arithmetic. Results: 104 patients with PCL injury had a mean slope of 5.7 ± 2.1° against 8.6 ± 2.2° in 104 matched controls, and “a flattened tibial slope of approximately < 6 degrees may increase the force on the PCL.” Interrater ICC 0.852, intrarater 0.872, two raters with a third measuring a random sample of 65. The Discussion adds that “an increased posterior tibial slope represents a risk factor for noncontact ACL injuries”, with no threshold given.
- Di Benedetto P, Buttironi MM, Mancuso F, Beltrame A, Gisonni R, Causero A. Anterior cruciate ligament reconstruction: the role of lateral posterior tibial slope as a potential risk factor for failure. Acta Biomed. 2020;91(Suppl 14):e2020024. A small MRI series — 36 patients, 26 female and 10 male — measured by Hudek’s method on sagittal T1 scans: “The angle between the line orthogonal to the longitudinal tibial axis of the MRI and the tangent to the lateral plate”. Mean lateral slope “10.9° on average”, “11.8” in women against “8.7°” in men. The figures this page quotes from it are the ones it reports from OTHER studies, and they were read here rather than in the primary papers: Christensen et al “found a greater lateral tibial slope in patients who had graft failure (8.4° versus 6.5°)” and “estimated an increased relative risk for graft failure of 1.6 with a 2° slope increase”, “2.4 with a 4° increase, and 3.8 with a 6° slope increase”; Webb et al “found an incidence close to 60% for graft rupture or contralateral ACL injury” “in patients with a tibial slope greater than 12°”. Webb’s cohort size is not stated in the text and is therefore not given here. Note also that an MRI slope and a radiographic slope are not interchangeable: the reference axis is constructed differently and the measured numbers in this series are higher than Bernhardson’s radiographic ones.
- Radiopaedia. Posterior tibial slope. Quoted for its numbers and NOT for its method. “Mean posterior tibial slope angle was around 7.7 degrees in medial compartment” “to that of 6.85 in lateral”, and “Increased (up to 5x) risk of further injury after ACL reconstruction with a posterior tibial slope of ≥12°” — an independent corroboration of the 12-degree figure this page’s upper band uses. Its method, however, is “drawing two lines both tangential of posterior tibial cortex and tibial plateau” with “The angle between the two lines” taken as the slope, with no perpendicular and no subtraction: read literally that returns an angle near 90° rather than near 7.7, and its reference is the posterior cortex rather than the proximal anatomical axis. The fetched page is about 1,000 characters long. This page therefore implements Bernhardson’s stated method.
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/