Turn Radius Calculator
Find an aircraft’s turn radius, rate of turn, time for a full circle and load factor from its true airspeed and bank angle. It also gives the bank for a standard-rate turn or for a radius you need, and how far the stall speed rises in the turn.
How to Use
- Choose what to find: Radius & rate from a bank angle, Bank for a rate (3°/s is a standard-rate turn), or Bank for a radius.
- Enter the true airspeed in knots, mph or km/h. The PHAK’s turn formulas use true airspeed, which is higher than indicated airspeed at altitude; the Airspeed Calculator converts.
- Enter the bank angle, the rate of turn or the radius you need. The answer appears in the highlighted field, in the unit you pick beside it.
- Optionally enter the 1-G stall speed from your POH to see how far it rises in the turn.
- Read the radius, rate, time for 360° and load factor, and compare the exact standard-rate bank with the Instrument Flying Handbook’s two rules of thumb.
Worked Example
The PHAK’s turn: 120 kt and 30° of bank. 120 kt is 61.73 m/s and tan 30° = 0.57735. Rate of turn ω = g × tan φ ÷ V = 9.80665 × 0.57735 ÷ 61.73 = 0.0917 rad/s = 5.25° per second, so a full circle takes 360 ÷ 5.25 = 68.5 s. Radius R = V² ÷ (g × tan φ) = 61.73² ÷ (9.80665 × 0.57735) = 673.1 m = 2,208 ft. Load factor 1 ÷ cos 30° = 1.15 G. The PHAK’s shortcut R = V² ÷ (11.26 × tan φ) with V in knots gives 2,215 ft; its constant is rounded (the exact value is 11.29), so it lands 0.3% long.
A standard-rate turn at 90 kt. 3° a second is 0.05236 rad/s, so tan φ = V × ω ÷ g = 46.30 × 0.05236 ÷ 9.80665 = 0.2472 and the bank is 13.9°, on a 2,901 ft radius at 1.03 G. The Instrument Flying Handbook gives two rules of thumb: 15% of the true airspeed, 13.5°, and “divide the airspeed by ten and add 7”, 16°. The second rule is 2.1° steep at 90 kt but meets the exact value near 140 kt (21.0°).
The common mistake: thinking twice the speed means twice the radius. At the same 30° of bank, 240 kt gives a radius of 8,833 ft, not 2 × 2,208 = 4,417 ft: the radius goes with the square of the speed, so it is four times as big. The rate halves to 2.63° a second and the full circle takes 137 seconds. To keep the same rate of turn at 240 kt you would need 49.1° of bank.
Show Work
Formulas
Why Banking Turns an Airplane
An airplane is not steered like a car. The PHAK explains that when it banks, lift tilts with the wings and splits into two parts: a vertical part that holds the airplane up against its weight, and a horizontal part that pulls it round the turn. Because only the vertical part now supports the weight, the wing has to make more lift to hold altitude, which is the load factor: 1 ÷ cos φ, slowly at first and then steeply, 2 G at 60° and 5.76 G at 80°. A level turn at 90° is impossible, because no lift would be left to hold the airplane up. More load factor means a higher stalling speed, which is why the PHAK warns that steep turns make stalls possible at seemingly safe speeds.
The standard-rate turn of 3° a second, a full circle in 2 minutes, is the reference for instrument flying. The Instrument Flying Handbook describes turn-and-slip indicators marked “2 MIN TURN”, on which the needle lined up with a doghouse mark means 3° a second, and notes that some instruments in faster aircraft are marked “4 MIN TURN”, where the same 3° a second takes two needle widths. Because the bank for a standard-rate turn grows with speed, the handbook gives rules of thumb to estimate it.
The PHAK’s shortcut constants come from the same physics in pilot units: 1,091 turns g ÷ V from radians per second with V in knots into degrees per second (the exact figure with standard gravity is 1,092.2), and 11.26 turns knots squared into feet (exactly 11.29). Every formula here assumes a coordinated, constant-altitude turn in still air and uses true airspeed, as the PHAK notes.
About This Calculator
This calculator solves the level, coordinated turn three ways: radius and rate from a bank angle, the bank for any rate of turn (with standard rate as the default), and the least bank for a radius. It works in SI with standard gravity (9.80665 m/s²), shows the PHAK’s shortcut answers beside the exact ones, sets the exact standard-rate bank next to both Instrument Flying Handbook rules of thumb, and adds the load factor and, if you enter it, the stall speed in the turn. It warns past 60° of bank and past the 3.8 G normal-category limit load factor. Sources: the Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C, chapter 5) and the Instrument Flying Handbook (FAA-H-8083-15B, chapters 4, 5 and 7).
The radius is over the air mass; wind drifts the circle over the ground. Everything runs in your browser and nothing you type is sent anywhere.
Related tools: Airspeed Calculator, Weight & Balance Calculator, and Heading Calculator.
For planning and training only — always use your aircraft’s POH/AFM and official weather and charts.
Frequently Asked Questions
What bank angle gives a standard-rate turn?
A standard-rate turn is 3° per second, a full circle in 2 minutes, and the bank it needs grows with speed: exactly 13.9° at 90 kt, 18.2° at 120 kt and 22.4° at 150 kt true airspeed. The Instrument Flying Handbook’s rule of thumb, 15% of the true airspeed, gives 13.5°, 18° and 22.5°.
How do you calculate turn radius?
For a level, coordinated turn the radius is the speed squared divided by g times the tangent of the bank: R = V² ÷ (g × tan φ). The PHAK writes it for knots and feet as R = V² ÷ (11.26 × tan φ). At 120 kt and 30° that is 2,215 ft by the PHAK’s constant and 2,208 ft exactly.
Why does doubling the speed quadruple the turn radius?
Because the radius goes with the square of the speed. At 30° of bank, 120 kt gives a 2,208 ft radius and 240 kt gives 8,833 ft, four times as much, while the rate of turn halves from 5.25° to 2.63° a second and a full circle takes 137 seconds instead of 68.5.
How much does the stall speed go up in a turn?
It goes up with the square root of the load factor. In a level 60° bank the load factor is 2 G, so the stall speed rises by √2, 41%: a 50 kt stall speed becomes 70.7 kt. The PHAK’s example: at 4 G an airplane that stalls at 50 kt in level flight stalls at 100 kt.
What is the load factor in a 60° bank?
Exactly 2 G in a level coordinated turn, since the load factor is 1 ÷ cos 60°. It is 1.15 G at 30°, 1.41 G at 45° and 5.76 G at 80°. The 3.8 G limit of a normal-category airplane is reached at 74.7°, which is why the PHAK calls about 60° the practical maximum for a level turn in most light airplanes.
How do I use the Turn Radius Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Instrument flying
A standard-rate turn at 120 kt true needs 18.2° of bank and has a 3,868 ft radius, about 0.64 nautical miles.
Steep turn practice
A 45° bank at 100 kt turns at 10.9° a second on an 885 ft radius, a full circle in 33 seconds, at 1.41 G.
Turning in a valley
To stay inside a 2,000 ft radius at 100 kt you need at least 23.9° of bank.
Stall margin in a turn
An airplane that stalls at 50 kt in level flight stalls at 70.7 kt in a 60° level turn.
Jet speeds
At 450 kt a 25° bank turns at only 1.13° a second on a radius of 6.33 nautical miles.
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