Turn Radius Calculator
Find how wide and how fast your aircraft turns at any speed and bank, and the bank you need for a standard-rate turn.
For example to stay inside a valley, a circuit or a protected area.
Wings-level stall speed for your weight and flap setting, from the flight manual. Uses the same unit as the airspeed.
The difference between the inbound and outbound tracks, to see how early to start a fly-by turn.
Every bank angle at 120 kt
How your turn is worked out
Turn the speed into feet or metres per second, then gravity and the bank angle do the rest.
- 1
Speed per second
120 kt × 1.688
= 202.5 ft/s - 2
Turn radius
202.5² ÷
(32.17 × tan 30°)
= 2,208 ft - 3
Rate of turn
32.17 × 0.577
÷ 202.5
= 5.25°/s
360° in 68.5 s - 4
Load factor
1 ÷ cos 30°
= 1.15 g
stall speed × 1.07
Read more: the formula, a worked example, rules of thumb and the lead-turn distance
When an aircraft banks, part of the wing's lift pulls it sideways into the turn. The steeper the bank, the harder that sideways pull and the tighter and quicker the turn. The faster you fly, the wider the circle. This calculator assumes a level, balanced (coordinated) turn at a steady true airspeed in still air.
The formula
turn radius = speed² ÷ (gravity × tan bank)
rate of turn (degrees per second) = gravity × tan bank ÷ speed × 57.3
time for 360° = 360 ÷ rate of turn
load factor = 1 ÷ cos bank
stall speed in the turn = stall speed at 1 g × √load factor
bank for a rate = atan(rate in radians per second × speed ÷ gravity)
bank for a radius = atan(speed² ÷ (gravity × radius))
lead-turn distance = turn radius × tan(course change ÷ 2)
Use speed in feet per second with gravity 32.17 ft/s², or metres per second with 9.81 m/s². 1 knot = 1.688 ft/s = 0.5144 m/s. In knots and feet the same formulas become: radius (ft) = knots² ÷ (11.29 × tan bank), and rate of turn = 1,092 × tan bank ÷ knots.
Worked example
At 120 kt and 30° of bank: 120 × 1.6878 = 202.54 ft/s. tan 30° = 0.5774, so the radius is 202.54² ÷ (32.174 × 0.5774) = 41,022 ÷ 18.576 = 2,208 ft (673 m, 0.36 NM). The diameter is 4,417 ft.
The rate of turn is 32.174 × 0.5774 ÷ 202.54 = 0.0917 radians per second × 57.3 = 5.25° per second, so a full circle takes 360 ÷ 5.25 = 68.5 s, a 180° turn 34.3 s and a 90° turn 17.1 s.
The load factor is 1 ÷ cos 30° = 1 ÷ 0.866 = 1.15 g, and √1.15 = 1.07, so a stall speed of 50 kt wings-level becomes 53.7 kt in this turn. For a standard-rate turn (3° per second = 0.05236 radians per second) at 120 kt you need atan(0.05236 × 202.54 ÷ 32.174) = atan(0.3296) = 18.2° of bank; the rule of thumb gives 120 ÷ 10 + 7 = 19°.
For a 90° course change at a fly-by waypoint, the lead distance is 2,208 × tan 45° = 2,208 × 1 = 2,208 ft: start rolling into the turn that far before the waypoint.
Rules of thumb
- Standard-rate bank: knots ÷ 10 + 7. It is close for light aircraft speeds and drifts a degree or two at higher speeds.
- Standard-rate radius: about knots ÷ 200 NM. The exact figure is knots ÷ 188.5 (that is, ÷ 60π), so 120 kt gives 0.64 NM.
- Twice the speed, four times the radius. Halve the speed and the turn is a quarter as wide.
- 60° of bank = 2 g. The stall speed is then 41% higher than wings-level.
- Above about 170 kt a standard-rate turn needs more than 25° of bank, so jets and autopilots often turn at a set bank (around 25°) instead of rate one. Instrument procedure design commonly assumes 25° or rate one, whichever needs less bank.
Load factor by bank angle
| Bank | Load factor | Stall speed rises by |
|---|---|---|
| 15° | 1.04 g | 2% |
| 30° | 1.15 g | 7% |
| 45° | 1.41 g | 19% |
| 60° | 2.00 g | 41% |
| 75° | 3.86 g | 97% |
Wind
The radius through the air doesn't change with wind, but over the ground the circle drifts downwind, so the track becomes a stretched loop. To hold a circle around a point on the ground, use the steepest bank when flying downwind (fastest ground speed) and the shallowest when flying into wind.
For planning, training and education. Fly the bank limits in your aircraft's flight manual and your operator's procedures.
Common questions
How do you calculate the turn radius of an aircraft?
Square the true airspeed and divide it by gravity times the tangent of the bank angle: radius = V² ÷ (g × tan bank). Use feet per second with 32.17 ft/s², or metres per second with 9.81 m/s². At 120 kt (202.5 ft/s) and 30° of bank the radius is about 2,208 ft, or 0.36 NM.
What bank angle gives a standard-rate turn?
A standard-rate (rate one) turn is 3° per second, so a full circle takes 2 minutes. The bank you need grows with speed. The quick rule is your airspeed in knots ÷ 10 + 7. At 120 kt that gives 19°, and the exact figure is 18.2°. A half-standard-rate turn at 120 kt needs about 9.4°.
How does bank angle affect load factor and stall speed?
In a level turn the load factor is 1 ÷ cos(bank), and the stall speed goes up by the square root of the load factor. At 30° you pull 1.15 g and the stall speed rises about 7%. At 45° it is 1.41 g and about 19%. At 60° it is 2 g and the stall speed is 41% higher.
How does airspeed change the turn radius?
The radius grows with the square of the speed. Double the speed at the same bank and the turn becomes four times as wide, while the rate of turn halves. At 30° of bank, 120 kt gives a radius of about 2,208 ft, and 240 kt gives about 8,833 ft.
How far before a waypoint should I start a turn?
For a smooth fly-by turn, start turning at the radius × tan(half the course change). For a 90° change the lead distance equals the radius, so at 120 kt and 30° of bank you would start about 2,208 ft before the waypoint. Small course changes need much less lead.
Does wind change the turn radius?
Not through the air. The radius and rate of turn depend only on true airspeed and bank. Over the ground, though, the wind carries the whole circle along, so the track is stretched downwind and the ground speed changes as you turn. For turns around a ground point, bank more when flying downwind and less when flying into the wind.
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Made by Zulu Calculator, part of AlphaZulu LLC. Formulas are shown in full and rule figures are checked against official sources; see how we build calculators.