Turn Rate Calculator for Engineering

Calculator

Method

Pick the inputs you already have.

Direction

Sign affects the reported angular velocity.

Speed

Turn Radius

Used for roads, robotics, and motion planning.

Bank Angle

Assumes coordinated turn (no sideslip).

Heading Change

Use with IMU logs or compass data.

Time

Lateral Acceleration

Useful when you have comfort or traction targets.

Optional safety checks

Leave blank to skip.

Max Turn Rate

Flags when the computed rate exceeds your limit.

Max Lateral g

g

Useful for comfort, cargo, and tire limits.

Reset

Results appear above this form after calculation.

Example Data

Scenario	Inputs	Expected Outputs (approx.)
Road vehicle	V=60 km/h, r=120 m	ω≈0.1389 rad/s, 7.96 deg/s, a≈2.31 m/s² (0.236 g)
Coordinated bank	V=120 knots, φ=25°	ω≈0.167 rad/s, 9.59 deg/s, r≈475 m
Heading log	Δψ=90°, Δt=6 s, V=10 m/s	ω≈0.262 rad/s, 15.0 deg/s, r≈38.2 m
Comfort target	V=20 m/s, a=0.30 g	ω≈0.147 rad/s, 8.41 deg/s, r≈136 m

Examples are illustrative; your results vary with units and precision.

Formulas Used

Speed + Radius: ω = V / r, a = V² / r
Heading + Time: ω = Δψ / Δt, r = V / |ω|, a = |ω|·V
Bank + Speed: ω = g·tan(φ)/V, r = V²/(g·tan(φ)), a = g·tan(φ)
Lateral Accel + Speed: a = ω·V ⇒ ω = a/V, r = V²/a

Where V is speed, r is turn radius, ω is angular velocity, a is lateral acceleration, g is 9.80665 m/s², and φ is bank angle.

How to Use

Select a method that matches your available measurements.
Enter speed and the method-specific inputs with units.
Optionally set maximum turn rate or lateral g limits.
Press Calculate to show results above the form.
Use the CSV or PDF buttons to export your report.

FAQs

1) What is turn rate?

Turn rate is how quickly heading changes, usually in deg/s or deg/min. It equals angular velocity expressed in degrees.

2) Which method should I choose?

Use speed+radius for path planning, heading+time for sensor logs, bank+speed for coordinated vehicle/aircraft turns, and lateral-accel+speed for comfort or traction targets.

3) Why do I see signed and magnitude values?

Signed ω keeps direction (left negative, right positive). Magnitude ignores direction and is used for timing and limit checks.

4) How is lateral acceleration computed?

For a circular path, lateral acceleration is a = V²/r. If ω is known, a can also be computed as a = |ω|·V.

5) Does the bank-angle method assume anything?

Yes. It assumes a coordinated turn with lift providing the required centripetal force. Real systems may need corrections for slip, drag, or control limits.

6) What if my heading change crosses 0/360 degrees?

Use the shortest intended change, such as −10° instead of +350°. The calculator treats the entered change directly.

7) Why might my results look too high?

Common causes are small radius values, high speed, or unit mistakes. Double-check conversions and consider adding the optional limit checks.

8) Can I use this for non-circular turns?

It best fits constant-radius, steady turns. For varying curvature, compute turn rate over short intervals and analyze the profile across time.