Bank Angle Calculator — Ideal Tilt for a Circular Turn
Find the ideal bank angle for any circular turn. Enter the speed, turn radius, and gravitational field to get the tilt angle that produces a perfectly coordinated turn with no sideways slip or side-force on passengers.
Speed unit
m
m/s²
Angle from horizontal that eliminates lateral slip in a coordinated turn
- 1
Speed in m/s
60 km/h ÷ 3.6 = 16.6667 m/s - 2
Centripetal acceleration
v² ÷ r = 16.6667² ÷ 200 = 1.3889 m/s² - 3
Ideal bank angle
arctan(1.3889 ÷ 9.81) = 8.06 °Tilt that eliminates lateral slip — the horizontal lift component equals centripetal acceleration.
How does this calculator work?
The ideal bank angle for a circular turn is θ = arctan(v²/(r·g)), where v is speed (m/s), r is turn radius (m), and g is gravity (9.81 m/s²). At this angle, lift or normal force is split exactly between supporting weight (vertical) and providing centripetal force (horizontal), with zero lateral slip. The load factor is n = 1/cos(θ).
Formula
How this is calculated
When a vehicle or aircraft moves in a circle, a centripetal force directed toward the centre of the turn is required. On a flat, level surface that force comes entirely from friction; on a banked surface the normal force (or aerodynamic lift) tilts inward and its horizontal component supplies the centripetal force without any sideways friction.
The ideal bank angle θ satisfies tan(θ) = v²/(r·g): the horizontal-to-vertical ratio of the lift equals the centripetal-to-gravitational acceleration ratio. At this precise angle the vertical lift component cancels weight and the horizontal component provides exactly the centripetal force needed for the turn, producing a smooth "coordinated" manoeuvre. Road engineers call this superelevation; pilots call it a coordinated bank; railway engineers call it cant.
The load factor n = 1/cos(θ) gives the apparent weight multiple experienced by occupants. At 30° bank n ≈ 1.15 g; at 45° n ≈ 1.41 g; at 60° n = 2 g; at 80° it reaches 5.76 g. Sustained high load factors fatigue structures and can cause G-LOC (g-induced loss of consciousness) in pilots above about 4–5 g. The formula assumes steady, symmetric circular motion; aerodynamic drag and thrust are not modelled.
Frequently asked questions
v = 100/3.6 ≈ 27.78 m/s; v²/r = 27.78²/250 ≈ 3.09 m/s²; θ = arctan(3.09/9.81) ≈ 17.5°. Road curves are rarely banked beyond 6–10% (≈3–6°), so the remaining centripetal force must come from tyre friction.
The load factor n = 1/cos(θ). At 45° bank the pilot feels 1.41 g; at 60° they feel 2 g. High-performance aerobatic manoeuvres can reach 9 g, requiring the pilot to use a G-suit to prevent blood from pooling in the legs.
Highways are "superelevated" (banked) on curves to reduce lateral friction demand on tyres. The ideal superelevation is e = v²/(r·g), expressed as a ratio (m/m). Design standards typically cap superelevation at 8–10% to avoid problems when vehicles are slow or stopped on the curve. Railways use a raised outer rail ("cant") calculated with the same formula.
TG we-Calculate Editorial Team. (2026). Bank Angle Calculator — Ideal Tilt for a Circular Turn [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bank-angle-calculator
TG we-Calculate Editorial Team. "Bank Angle Calculator — Ideal Tilt for a Circular Turn." TG we-Calculate. 2026. https://we-calculate.com/calculator/bank-angle-calculator.
TG we-Calculate Editorial Team, "Bank Angle Calculator — Ideal Tilt for a Circular Turn," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bank-angle-calculator
@misc{wecalculate_bank_angle_calculator, title = {Bank Angle Calculator — Ideal Tilt for a Circular Turn}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bank-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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