Ship Turning Radius Calculator
Calculate an approximate ship turning radius using either speed and rate of turn, or the diameter of the vessel's turning circle.
Ship Turning Radius Result
How do you calculate ship turning radius?
For a vessel making a steady turn, turning radius can be calculated from its linear speed and angular rate of turn.
$$R = \frac{V}{\omega}$$
When ship speed is in knots and rate of turn is in degrees per minute, the result can be written directly in nautical miles:
$$R_{NM} = \frac{0.95493 \times V_{kn}} {ROT_{deg/min}}$$
What is the ship turning radius formula?
Converting the result into meters:
$$R_m = \frac{0.95493 \times V_{kn}} {ROT} \times 1852$$
This method assumes speed and rate of turn remain approximately constant during the turn.
How do you calculate turning radius from turning circle diameter?
If the vessel's maneuvering data provide the turning-circle diameter:
$$R = \frac{D}{2}$$
For example, a tactical turning-circle diameter of 720 m gives a radius of 360 m.
Ship turning radius example
Suppose a ship is travelling at 12 knots with a steady rate of turn of 10° per minute.
$$R = \frac{0.95493 \times 12}{10} = 1.146\ NM$$
Converting to meters:
$$1.146 \times 1852 \approx 2122\ m$$
What is a tactical diameter?
Tactical diameter is a standard maneuvering characteristic describing the lateral distance between the original track and the ship's heading after a 180-degree change during a turning maneuver.
It should not automatically be treated as exactly twice the steady turning radius because a real ship's maneuvering path is affected by advance, transfer, drift, rudder action, propeller effects, and hull dynamics.
What is the difference between turning radius and tactical diameter?
A turning radius describes the radius of an idealized or steady circular path. Tactical diameter is a measured maneuvering-trial parameter for an actual ship turning maneuver.
$$Idealized\ Circle\ Diameter = 2R$$
For real maneuvering analysis, use the vessel's maneuvering booklet, sea-trial results, or approved maneuvering data.
How does ship speed affect turning radius?
If rate of turn remains constant, increasing speed increases the radius proportionally.
$$V \uparrow \Rightarrow R \uparrow \quad (ROT\ constant)$$
How does rate of turn affect turning radius?
At constant speed, a higher rate of turn produces a smaller radius.
$$ROT \uparrow \Rightarrow R \downarrow \quad (V\ constant)$$
Ship turning radius chart
The table below assumes a constant ship speed of 10 knots.
| Rate of Turn | Approx. Radius | Approx. Diameter |
|---|---|---|
| 5°/min | 1.910 NM | 7,075 m |
| 10°/min | 0.955 NM | 3,538 m |
| 15°/min | 0.637 NM | 2,359 m |
| 20°/min | 0.477 NM | 1,769 m |
| 25°/min | 0.382 NM | 1,415 m |
| 30°/min | 0.318 NM | 1,179 m |
What factors affect a real ship's turning radius?
- Ship speed
- Rudder angle
- Hull form and underwater geometry
- Draft and trim
- Displacement
- Water depth
- Current and wind
- Propeller configuration
- Thrusters and steering system
Does shallow water change turning radius?
Yes. Shallow water can significantly change a ship's maneuvering behavior. The vessel may experience increased resistance and altered hydrodynamic forces, so a turning result measured in deep water should not automatically be assumed valid in shallow water.
Is turning radius the same as advance and transfer?
No. Advance and transfer are separate maneuvering characteristics. Advance describes the distance travelled in the original direction before a specified heading change, while transfer describes the lateral displacement from the original track.
Ship turning radius FAQ
For a steady turn, R = V / ω. With speed in knots and rate of turn in degrees per minute, R in nautical miles is approximately 0.95493 × V ÷ ROT.
Divide linear speed by angular velocity after converting the units consistently. At a constant speed, a higher rate of turn means a smaller radius.
It depends on the ship's speed, rudder angle, hull, draft, propeller arrangement, and water conditions. It can be calculated from measured rate of turn or taken from maneuvering trials.
No. Tactical diameter is a specific maneuvering-trial measurement, while turning diameter is the diameter of an idealized circular turning path.
As a simple geometric approximation, divide the turning-circle diameter by two. For detailed maneuvering analysis, use the vessel's actual trial data.