Highway & Railway Engineering
Superelevation Calculator
Design the full superelevation transition for highway curves — superelevation rate, runoff length, tangent runout, total transition development and edge-of-pavement profile — using the AASHTO maximum-relative-gradient method, with NHA Pakistan, IRC and BS limits.
Superelevation Calculator
e Rate · Runoff Length · Tangent Runout · Transition Development · Edge Profile Settings
Superelevation Rate
Radius of the horizontal curve
Transition Geometry (Runoff & Runout)
Width of one traffic lane
Lanes rotated about the axis
Adverse cross-slope removed in runout
Fraction of runoff placed before PC
Transition Table Interval
Designing the curve geometry itself (PC, PT, tangent, degree of curve)?
Use the Horizontal Curve Calculator —
this page focuses on the superelevation transition that develops into that curve.
Method
How Superelevation & Its Transition Are Designed
Superelevation is the banking of the carriageway toward the inside of a horizontal curve so that a component of gravity helps balance centrifugal force. But the curve cannot jump from a flat cross-slope to full banking instantly — it is developed gradually over a transition made of the tangent runout and the superelevation runoff. This calculator sizes that whole transition.
Determine the Design Superelevation Rate e
From the point-mass equation e + f = V²/(127R) (metric). Solve for e using the design speed, radius and the side-friction factor f. The rate must not exceed emax for the region (0.07 on NHA highways).Read the Maximum Relative Gradient Δ
Δ is the steepest allowable longitudinal slope between the pavement edge and the axis of rotation. It decreases with design speed (AASHTO Table 3-15): 0.60% at 60 km/h down to 0.38% at 120 km/h. A flatter Δ at high speed forces a longer, gentler transition.Compute the Superelevation Runoff Lr
The length to rotate the pavement from zero cross-slope to full superelevation: Lr = (w · n₁ · ed / Δ) · bw, where w is lane width, n₁ the number of rotated lanes, ed the design rate, and bw the multilane adjustment factor.Compute the Tangent Runout Lt
The length to remove the adverse (normal) crown before runoff begins: Lt = (eNC / ed) · Lr, using the same edge-rotation rate. The total transition length is Lt + Lr.Position the Transition Relative to the Curve
For an unspiralled curve, about two-thirds of the runoff (AASHTO: 0.67–0.80) is placed on the tangent before PC and the remainder on the curve, so full superelevation is reached just inside the curve.Plot the Edge-of-Pavement Profile
The development diagram shows the outside and inside edges rotating about the chosen axis through normal crown → runout → runoff → full superelevation, which is what the field crew sets out.∑ Core Superelevation Formulas
SUPERELEVATION DESIGN — AASHTO max-relative-gradient method
Design rate: e + f = V² / (127·R) (V km/h, R m)
Solve for e: e = V²/(127R) − f (cap at e_max)
Minimum radius: R_min = V² / [127·(e_max + f)]
Multilane factor: b_w = (1 + 0.5(n₁ − 1)) / n₁
Superelev. Runoff: L_r = (w · n₁ · e_d / Δ) · b_w
Tangent Runout: L_t = (e_NC / e_d) · L_r
Total Transition: L_total = L_t + L_r
Runoff on tangent: L_r,tan = p · L_r (p ≈ 0.67)
Runoff on curve: L_r,crv = (1 − p) · L_r
w = lane width n₁ = lanes rotated
e_d = design superelevation Δ = max relative gradient
e_NC= normal crown slope p = proportion on tangent
Imperial: replace 127 with 15 (V in mph, R in ft).
Reference
The Four Stages of Superelevation Development
Every superelevation transition moves the pavement through these stages in order.
| Stage | What Happens | Length | End Condition |
|---|---|---|---|
| Normal Crown | Both lanes drain away from centerline at the normal cross-slope | — | Outer lane at −eNC |
| Tangent Runout | Outer lane rotates up from −eNC to level (0%) | Lt | Pavement is a single flat plane |
| Superelevation Runoff | Whole section rotates from 0% to full ed | Lr | Full superelevation ed reached |
| Full Superelevation | Constant banking maintained around the curve | (curve) | Held until the exit transition |
For NHA Pakistan motorways, AASHTO development applies with emax=0.07 and
rotation usually about the median edge or centerline. On divided carriageways each direction is treated
separately. The axis of rotation changes which edges move, but the runoff length Lr depends on
the number of lanes rotated, not the axis.
Standards
AASHTO Maximum Relative Gradient (Δ) by Design Speed
The maximum relative gradient between the pavement edge and the axis of rotation. Lower values at higher speed produce longer, smoother runoffs. From AASHTO Green Book 2018, Table 3-15.
| Design Speed | Max Relative Gradient Δ | Typical Runoff (e=0.06, 2 lanes) | Use |
|---|---|---|---|
| 50 km/h | 0.65% | ≈ 50 m | Collector |
| 60 km/h | 0.60% | ≈ 54 m | Arterial |
| 70 km/h | 0.55% | ≈ 59 m | Secondary highway |
| 80 km/h | 0.50% | ≈ 65 m | National highway |
| 90 km/h | 0.47% | ≈ 69 m | NHA highway |
| 100 km/h | 0.44% | ≈ 74 m | Motorway |
| 110 km/h | 0.41% | ≈ 79 m | Motorway |
| 120 km/h | 0.38% | ≈ 85 m | M-roads (M-1, M-2) |
Runoff column assumes lane width 3.6 m, ed=0.06, 2 lanes rotated
(bw=0.75). Always confirm Δ and emax against the project authority's manual.
Worked Example
Superelevation Transition — NHA Motorway Curve
Problem: A 2-lane (each direction) motorway curve has R = 400 m, design speed 100 km/h, emax = 0.07, lane width 3.6 m, normal crown 2%. Rotation about centerline, 0.67 of runoff on tangent. Find e, runoff, tangent runout and total transition.
Given:
R = 400 m V = 100 km/h e_max = 0.07 w = 3.6 m
n1 = 2 e_NC = 0.02 Δ = 0.44% p = 0.67 f = 0.12
Step 1 — Design Superelevation Rate:
e = V²/(127R) − f = 100²/(127·400) − 0.12
= 10000/50800 − 0.12 = 0.1969 − 0.12 = 0.0769
e exceeds e_max 0.07 → adopt e_d = 0.07 (curve near minimum radius)
Step 2 — Multilane Adjustment Factor:
b_w = (1 + 0.5(n1−1))/n1 = (1 + 0.5)/2 = 0.75
Step 3 — Superelevation Runoff:
L_r = (w·n1·e_d/Δ)·b_w
= (3.6·2·0.07 / 0.0044)·0.75
= (0.504 / 0.0044)·0.75 = 114.55·0.75 = 85.9 m
Step 4 — Tangent Runout:
L_t = (e_NC/e_d)·L_r = (0.02/0.07)·85.9 = 24.5 m
Step 5 — Total Transition:
L_total = L_t + L_r = 24.5 + 85.9 = 110.4 m
Step 6 — Position Relative to PC:
Runoff on tangent = 0.67·85.9 = 57.6 m (before PC)
Runoff on curve = 0.33·85.9 = 28.3 m (after PC)
ANSWER: e_d = 0.07 | L_r = 85.9 m | L_t = 24.5 m
Total transition = 110.4 m
Place 57.6 m of runoff before PC, 28.3 m beyond PC.
Practice
Expert Tips for Superelevation Design
Rate & Limits
- Cap e at emax (0.07 NHA). If the required e exceeds it, the radius is too sharp — lengthen the curve, don't over-bank
- Below a minimum-radius threshold for the speed, AASHTO keeps the road at normal crown — no superelevation needed
Runoff Length
- Use the max-relative-gradient method, not a fixed length — high-speed roads need much longer runoffs
- More rotated lanes increase Lr, but the bw factor keeps it less than proportional
- Round the final Lr up to a practical setting-out length
Positioning
- Place ~0.67–0.80 of runoff on the tangent so full superelevation is just reached inside the curve
- On spiralled curves, develop the full runoff along the spiral length instead
Drainage & Comfort
- Watch the zero-cross-slope point in the runoff — flat pavement drains poorly; keep a min profile grade ≥ 0.5%
- Avoid placing the cross-slope reversal on a low point of the vertical profile
Final superelevation and transition design must be verified and signed by a
licensed Civil / Transport Engineer. This calculator is for preliminary design and checking only.
FAQ
Frequently Asked Questions
Tangent runout (Lt) is the length needed to rotate the outside lane from its normal
adverse crown up to a level (zero) cross-slope. Superelevation runoff (Lr) is the length needed
to then rotate the whole pavement from level up to the full design superelevation. The full transition is
the sum of both, Lt + Lr.
By the AASHTO maximum-relative-gradient method: Lr = (w · n₁ · ed / Δ) · bw,
where w is lane width, n₁ the number of lanes rotated, ed the design superelevation rate, Δ the
maximum relative gradient for the design speed, and bw = (1 + 0.5(n₁−1))/n₁ the multilane
adjustment factor.
Δ is the maximum allowable longitudinal slope of the pavement edge relative to the axis of
rotation. AASHTO tabulates it against design speed — for example 0.60% at 60 km/h falling to 0.38% at
120 km/h. The lower value at higher speed forces a longer, smoother runoff for ride comfort and appearance.
For curves without a spiral, AASHTO recommends placing about 0.67 to 0.80 of the runoff length
on the tangent ahead of PC, with the remainder on the curve. This means full superelevation is achieved a
short distance inside the curve, which gives the smoothest driver path.
Pakistan's NHA follows AASHTO geometric design with maximum superelevation emax = 0.07
for motorways and national highways. Provincial roads also reference IRC, which allows up to 0.10 in hilly
terrain. The runoff and runout are developed by the AASHTO max-relative-gradient method in both cases.
No — the runoff length depends on the number of lanes rotated (through n₁ and bw),
not on whether you rotate about the centerline, the inside edge or the outside edge. The axis only changes
which edges move and the resulting edge-elevation profile, which is why the development diagram differs by
method even when Lr is identical.
