Enter the velocity of the aircraft and the bank angle into the calculator to determine the aircraft turn radius.
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Aircraft Turn Radius Formula
The calculator uses the level, coordinated turn equations. Pick the formula that matches the inputs you have.
r = V^2 / (g * tan(phi))
omega = g * tan(phi) / V
phi = arctan(V^2 / (g * r))
n = 1 / cos(phi)
- r = turn radius
- V = true airspeed (or ground speed for ground-track radius)
- phi = bank angle
- omega = turn rate (radians per second; multiply by 180/pi for degrees per second)
- g = 9.80665 m/s²
- n = load factor in G
The formulas assume a level, coordinated turn with no wind effects on the air-mass radius. Use ground speed if you want the radius traced over the ground. Speeds are converted to m/s internally before calculation.
Reference Values
Common bank angles, the resulting load factor, and the radius they produce at typical airspeeds.
| Bank | Load factor | Radius at 100 kn | Radius at 250 kn | Radius at 450 kn |
|---|---|---|---|---|
| 15° | 1.04 G | 3,225 ft | 20,160 ft | 65,300 ft |
| 25° | 1.10 G | 1,855 ft | 11,580 ft | 37,520 ft |
| 30° | 1.15 G | 1,495 ft | 9,355 ft | 30,290 ft |
| 45° | 1.41 G | 865 ft | 5,400 ft | 17,490 ft |
| 60° | 2.00 G | 500 ft | 3,120 ft | 10,100 ft |
Standard rate turn references used in instrument flight.
| Term | Turn rate | 360° time | Bank rule of thumb |
|---|---|---|---|
| Standard rate | 3°/s | 2 min | TAS/10 + 7 |
| Half standard | 1.5°/s | 4 min | TAS/20 + 7 |
Worked Example
An aircraft at 140 knots true airspeed in a 30° bank.
- Convert speed: 140 kn = 72.02 m/s
- tan(30°) = 0.5774
- r = 72.02² / (9.80665 × 0.5774) = 916 m, or about 3,005 ft
- Turn rate = 72.02 / 916 = 0.0786 rad/s = 4.5°/s
- Time for 360°: 80 seconds
- Load factor: 1 / cos(30°) = 1.15 G
FAQ
Does this account for wind? No. The formula gives the radius through the air mass. In wind, the ground track becomes a distorted curve even at constant bank.
True airspeed or indicated? Use true airspeed for the air-mass radius. Indicated airspeed under-reports at altitude and will give a smaller radius than the aircraft actually flies.
Why does the result change with altitude? It changes only because TAS rises with altitude for the same indicated airspeed. The geometry itself depends only on V, g, and bank angle.
What bank is too steep? Above 60° the load factor exceeds 2 G and stall speed rises by more than 40%. Verify the maneuver is within aircraft limits and pilot training.
