Turn Radius & Bank Angle
Airspeed and bank angle give turn radius, rate of turn and the turn geometry drawn to scale.
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Choose what you know — the bank angle, the rate of turn or the radius — and set the true airspeed. The circle is drawn to scale on nautical-mile rings and the aircraft flies around it at the computed rate in real time, so a standard-rate turn visibly takes two minutes while a 45° steep turn at the same speed is over in half the time.
Drag the amber handle on the circle to ask the opposite question: “what bank do I need for this radius at this speed?”. The panel in the corner shows how the radius grows with the square of the airspeed at a fixed bank — the reason a fast aircraft needs a longer lead when intercepting a course (IFH ch. 4).
Watch the load factor: it depends on the bank alone (1.15 G at 30°, 1.41 G at 45°, 2 G at 60°) and raises the stall speed by its square root. The standard-rate bank line links to the Standard Rate Turn tool.
Assumption: a coordinated, constant-altitude turn in still air with an instantaneous roll; radius and rate use true airspeed (groundspeed over the ground in calm air). Wind changes the ground track, not the relations shown here.
Coordinated level turn: r = V² / (g·tan φ), rate ω = g·tan φ / V, load factor n = 1 / cos φ, with g = 9.80665 m/s² and 1 kt = 0.514444 m/s (exact SI relations, radius in NM and ft). Inverse forms: φ = atan(ω·V / g) for a given rate, φ = atan(V² / (g·r)) for a given radius. The radius and rate are the same calculations the IFR Trainer uses, so this tool and the DME Arc / Holding / Procedure Turn trainers draw the same turn geometry.
Verified: PHAK ch. 5 Figure 5-59 (120 kt, 30° bank → 2,215 ft) and the IFH ch. 4 engineering forms rate = 1,091·tan φ / V (°/s) and r = V² / (11.26·tan φ) (ft) agree with the exact relations within 0.5 % (their constants are rounded); PHAK Figure 5-53 load factors (30° → 1.15 G, 45° → 1.41 G, 60° → 2 G, 70.5° → 3 G); standard rate at 120 kt → 18.3°.
Limits: bank 1°–75° (3.9 G at 75°) and TAS 40–500 kt are the control ranges; a requested rate or radius that needs more than 60° of bank is shown with a warning, never hidden.
- FAA Pilot’s Handbook of Aeronautical Knowledge, FAA-H-8083-25C (2023), ch. 5 Aerodynamics of Flight — Figure 5-53 (load factor vs bank: 60° = 2 G), Figure 5-56 (rate of turn), Figure 5-59 (radius of turn: 120 kt at 30° = 2,215 ft)
- FAA Instrument Flying Handbook, FAA-H-8083-15B (2012), ch. 4 Aerodynamic Factors — “Rate of Turn”, “Radius of Turn”, Figure 4-15; standard rate 3°/s
- Cross-tool: the same turn radius and rate of turn as the IFR Trainer’s DME Arc, Holding and Procedure Turn modules