Turn radius from speed, bank angle, or turn rate

This turn radius calculator converts speed plus either a coordinated bank angle or a measured turn rate into a practical radius. It supports metres per second, kilometres per hour, miles per hour, and knots, and reports the result in metres, kilometres, and feet. Signed angles and rates also preserve left or right turn direction. Use it for flight planning, vehicle path estimates, simulator checks, or a quick comparison of how speed and control input change the space required to turn.

Choose the input that matches the information you have

Start with a positive speed and select its actual unit. Then provide exactly one turning input. Use bank angle when planning a coordinated, level aircraft turn in still-air conditions, or when exploring how a chosen bank affects the ground-space estimate under a simplified model.

Use turn rate when you already know angular motion from an instrument, simulation, route requirement, or vehicle log. A positive bank angle or turn rate is reported as a right turn, while a negative value is reported as a left turn; the radius itself remains a positive distance. Do not enter both turning inputs, because they represent two different ways of defining the same motion and may conflict.

Zero bank and zero turn rate describe straight travel with an unbounded radius, so the calculator rejects them rather than returning a misleading finite value. Units matter: 120 knots is very different from 120 kilometres per hour, even though the numeric speed is identical. Check the selected unit before using the result in a route, safety margin, or map overlay.

Understand the formulas and assumptions

For the bank-angle method, the calculator applies the standard coordinated-turn relationship: radius equals speed squared divided by gravitational acceleration times the tangent of the absolute bank angle. Speed is converted to metres per second before calculation, and gravity defaults to standard gravitational acceleration. You may supply another positive gravity value when modelling a different assumption.

For the turn-rate method, radius equals linear speed divided by angular speed, with degrees per second converted to radians per second. The calculator also derives the complementary turn rate or bank angle so that results can be compared between methods. These equations describe ideal kinematics.

The coordinated-bank equation assumes level flight, balanced forces, constant speed, and no wind correction. It does not model climb angle, sideslip, tire friction, road superelevation, steering geometry, transient roll, or pilot reaction. The turn-rate equation is more general kinematically, but its accuracy still depends on the supplied rate and speed describing the same instant and reference frame.

Treat the output as a planning quantity, not as a substitute for certified performance data or operating procedures.

Interpret the radius and apply a suitable margin

The returned radius is measured from the centre of the circular path to the moving object's assumed reference point. Diameter is twice that value and is often easier to compare with available corridor width or map clearance. Results appear in metres, kilometres, and feet to reduce manual conversions, while the normalized speed in metres per second makes the calculation auditable.

Notice that the bank-angle formula contains speed squared: doubling speed at the same bank angle makes the radius four times larger. By contrast, radius at a fixed turn rate grows directly with speed. Those relationships make the calculator useful for sensitivity checks—run several realistic speeds and controls rather than relying on one nominal case.

Real operations need extra allowance for wind, tracking error, response delay, surface conditions, navigation tolerance, obstacle clearance, vehicle dimensions, and local rules. For aircraft, compare the estimate with the approved flight manual, operator guidance, airspace requirements, and actual conditions. For ground vehicles, account for the swept path of every body corner and trailer, not only the centreline radius.