Standard-rate bank, turn radius, and load factor
In a coordinated, level turn the airplane’s lift is tilted, so the horizontal component provides the centripetal acceleration and the wings must make more lift than the weight. The standard relationships, using true airspeed V and bank angle φ, are:
rate of turn ω = g tan φ / V
turn radius r = V² / (g tan φ)
load factor n = 1 / cos φ
stall speed in the turn = Vs × √n
A standard-rate turn is 3° per second (360° in two minutes). Solving the first equation for bank gives the exact standard-rate bank, about 15.4° at 100 kt and 18.2° at 120 kt. The rule of thumb taught in many courses is bank ≈ TAS/10 + 7 with TAS in knots (100 kt → 17°, 120 kt → 19°). The rule is a little conservative at typical light-airplane speeds and a little low at high TAS; this page always shows the exact angle next to it.
A compact published approximation for rate of turn is °/s ≈ 1,091 × tan φ / TAS(kt), which matches the exact formula to a few hundredths of a degree per second.
Worked examples
- 120 kt, standard rate: exact bank ≈ 18.2° (rule of thumb 19°), a 360° turn in 2 minutes, radius ≈ 0.64 nm (the circumference is 120 kt × 2 minutes).
- 60° bank: load factor = 2.0, stall speed increases by a factor of √2, or +41%.
- 45° bank: load factor ≈ 1.41, stall speed +19%. 30° bank: load factor ≈ 1.15, stall speed +7%.
How to use it
- Enter true airspeed. If you only have an indicated value, convert it with the true airspeed calculator.
- Choose a standard-rate turn, or type a bank angle or a desired rate.
- Optionally enter a level-flight stall speed to see the stall speed in that bank.
- Use the radius when you brief a hold, a procedure turn, or obstacle clearance, and remember that wind will blow the ground path away from the still-air circle. The wind triangle does not replace a wind-corrected hold entry, but it will give you the TAS and wind you started from.
Frequently asked questions
What bank angle is a standard-rate turn?
A standard-rate (Rate 1) turn is 3° per second, or a 360° turn in 2 minutes. The exact bank is arctan(TAS × ω / g), about 18.2° at 120 kt. The common rule of thumb is TAS in knots divided by 10, plus 7 (120 kt → 19°). This page shows both.
How do I calculate turn radius?
In a coordinated level turn, radius = V² / (g tan φ), using true airspeed. At a standard rate the radius is also V / ω, and a two-minute turn has a circumference of groundspeed (or TAS, in still air) times two minutes.
How much does stall speed increase in a bank?
Load factor in a level turn is 1 / cos(bank). Stall speed increases by the square root of that load factor. In a 60° bank the load factor is 2, so stall speed rises by a factor of √2, or about 41%. A 45° bank is about a 19% increase; a 30° bank is about 7%.
Do I use indicated or true airspeed?
Use true airspeed for radius and rate of turn — the geometry is about speed through the air (or over the ground, in a no-wind mental picture). Convert IAS or CAS first with the true airspeed calculator. Stall speed may be entered as the indicated or calibrated stall speed from the POH; the factor √n still applies.