Calculate bank angle, turn radius, load factor, and turn rate for aircraft or vehicles in coordinated turns. Includes G-force and stall speed factor.
The **Bank Angle Calculator** computes the geometry and forces of a coordinated (constant-altitude) banked turn. Given speed and turn radius, it finds the required bank angle; or given bank angle and speed, it finds the resulting radius. It also calculates load factor (g), turn rate, time to complete 360°, centripetal force, and the stall-speed increase in the turn.
Banked turns appear everywhere: aircraft, racecars, motorcycles, and even banked roads. The physics is the same — the horizontal component of the lift (or friction) force provides the centripetal acceleration needed for circular motion. As the bank angle increases, so does the load factor and the stall speed, making steep turns more dangerous.
Use the built-in aircraft presets or enter custom values. The reference tables show how bank angle, G-force, and radius interact across a range of speeds and angles, making this an invaluable tool for pilots, automotive engineers, and physics students.
Whether you are a pilot planning a holding pattern, an engineer designing a banked curve, or a student studying circular motion, this calculator delivers instant results for the full set of turn aerodynamics and forces.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Bank Angle: φ = arctan(v² / (g R)) Turn Radius: R = v² / (g tan φ) Load Factor: n = 1 / cos φ Turn Rate: ω = g tan φ / v [rad/s] Stall Speed Factor: √n where v = speed, g = 9.81 m/s², R = radius, φ = bank angle.
Result: 14.0° bank, 1.031 g load factor, 133 s per 360°
A Boeing 737-class aircraft at 250 km/h in a 2 km radius turn needs about 14° of bank, experiencing 1.03 g — barely noticeable to passengers.
Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.
Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.
Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.
A turn where the aircraft's bank angle is matched to its speed and radius so there is no sideslip — the ball in the turn-and-slip indicator stays centred. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
The vertical component of lift must still support weight, so total lift (and load factor) must increase as the wing tilts. Use this as a practical reminder before finalizing the result.
60° of bank produces a load factor of exactly 2 g in a coordinated turn. Keep this note short and outcome-focused for reuse.
At higher speed, a larger radius or steeper bank is needed; turn rate actually decreases for a given bank angle as speed increases. Apply this check where your workflow is most sensitive.
On a banked road, yes. The road tilt replaces wing-generated lift for the horizontal force component.
Commercial airliners are typically limited to 25–30° bank. Emergency manoeuvers may use up to 45°.