Turn radius calculator
How much room does a turn take? Only two things decide it: how fast you are going and how steeply you bank. Aircraft type and weight do not come into it at all.
Calculator
This is an educational and planning aid. Use current official weather, your aircraft flight manual, and the rules that apply to your flight before you act on any figure here. See the aviation disclaimer.
What the result means
The radius is the distance from the centre of the turn to the aircraft. The diameter is what matters when you are trying to fit a turn inside a valley or a piece of airspace.
The rate of turn is how many degrees per second you sweep through. Three degrees per second is a standard rate turn, which takes two minutes for a full circle.
Load factor in a level turn is set by bank angle alone. At 60 degrees of bank it is 2 g, regardless of aircraft or speed, and the stall speed rises by the square root of that.
When this is useful
- Judging whether a turn will fit inside controlled airspace or a valley.
- Understanding why a fast aircraft needs so much more room than a slow one.
- Seeing how sharply load factor and stall speed rise as bank angle increases.
How it is calculated
In a coordinated level turn, the horizontal component of lift provides the centripetal force. Setting that equal to mass multiplied by the square of velocity over radius, the mass cancels out, leaving radius as velocity squared divided by gravity multiplied by the tangent of the bank angle.
The mass cancelling is why a light trainer and a heavy jet at the same speed and bank angle carve exactly the same circle.
radius = velocity squared / (9.80665 x tan(bank angle))
Worked example
- True airspeed
- 100 kt
- Bank angle
- 30 degrees
The radius is about 1,530 ft, or 0.25 NM. The rate of turn is 6.3 degrees per second and the load factor is 1.15 g.
Check: Published figures for a 100 kt aircraft at 30 degrees of bank give a radius of about 1,530 ft, which matches. The load factor check is independent: 1 divided by the cosine of 30 degrees is 1.1547, exactly as shown.
Limitations
- It assumes a coordinated, constant altitude turn. A slipping or skidding turn, or a climbing or descending one, does not follow this geometry.
- It uses true airspeed. At altitude, true airspeed is well above indicated, so turns take far more room than the dial suggests.
- It says nothing about whether your aircraft can safely fly that bank angle at that speed. Stall speed rises with load factor.
Common mistakes
- Using indicated airspeed at altitude, which understates the radius considerably.
- Assuming a heavier aircraft turns more widely at the same speed and bank. It does not.
- Forgetting that doubling speed quadruples the radius, because velocity is squared.
Sources
- Pilot's Handbook of Aeronautical Knowledge, aerodynamics of flight , US Federal Aviation Administration