Rate of Turn Calculator

In a banked turn, how fast your heading swings around comes down to two things: how steeply you bank and how fast you're flying. This calculator works out the rate from those two numbers, or runs it backward to find the bank angle or airspeed you'd need for a given turn rate. Enter your bank angle and true airspeed to start.

What is Rate of Turn?

Turn rate is how quickly the nose swings around in a coordinated turn, measured in degrees per second. The number pilots care about most is the standard rate turn: 3 degrees per second, which takes an aircraft all the way around a 360-degree circle in exactly two minutes.

Two things set that rate: bank angle and airspeed. Bank steeper and more of the wing's lift points sideways, which hauls the nose around faster. Fly faster and the aircraft carves a wider circle, so the heading changes more slowly. Controllers and pilots lean on standard turn rates during approaches and holding patterns because predictable turns make spacing predictable.

How to Use This Calculator

Enter the bank angle, the tilt of the wings relative to the horizon. For general aviation turns this usually sits between 15 and 30 degrees.
Enter the aircraft's true airspeed. Switch between knots, km/h, mph, or m/s using the unit selector.
Read the Rate of Turn in whichever unit you picked.

You can also solve in reverse: enter the desired turn rate and airspeed to find the required bank angle, or enter the turn rate and bank angle to find the corresponding airspeed.

Understanding the Formula

The rate comes straight out of circular motion. In a coordinated bank, the horizontal slice of the wing's lift supplies the centripetal force that bends the flight path into a curve:

ROT = \frac{g \cdot \tan(\theta)}{V}

Where ROT is the rate of turn, g is gravitational acceleration ( $9.80665 \text{ m}/ \text{s}^2$ ), $\theta$ is the bank angle, and V is the true airspeed.

Say you're flying a Cessna at 120 knots (61.7 m/s) and roll into a 20-degree bank:

ROT = \frac{9.81 \times \tan(20^\circ)}{61.7} = \frac{9.81 \times 0.364}{61.7} = \frac{3.57}{61.7} \approx 0.058 \text{ rad/s}

Converting to degrees per second: $0.058 \times \frac{180}{\pi} \approx 3.3^\circ/s$ . That's very close to the standard rate turn of $3\degree/\text{s}$ . General aviation aircraft at typical cruise speeds need roughly a 20-degree bank for a standard rate turn.

The formula can also be rearranged to solve for bank angle: $\theta = \arctan\left(\frac{ROT \cdot V}{g}\right)$ , or for velocity: $V = \frac{g \cdot \tan(\theta)}{ROT}$ .

Practical Applications

Application / Field	Use Case
Instrument Flying	Pilots use standard rate turns during IFR procedures. Knowing the turn rate helps maintain precise heading changes during approaches and holding patterns.
Flight Planning	Navigation software and flight simulators use this formula to predict aircraft trajectories during turns.
ATC Operations	Controllers expect standard rate turns and factor them into spacing between aircraft on approach.
Aircraft Design	Engineers consider turn performance when designing handling characteristics and autopilot systems.

Tips for Pilots

Quick rule of thumb for a standard rate turn bank angle: divide your airspeed in knots by 10 and add 7. At 120 knots, that gives 12 + 7 = 19 degrees.
Bank angles above 30 degrees significantly increase the load factor and stall speed. Standard rate turns rarely need more than 25 degrees of bank.
At higher speeds, you need a steeper bank to maintain the same turn rate. Jets at 250 knots need about 32 degrees of bank for a standard rate turn.

Frequently Asked Questions

What is a standard rate turn?

A standard rate turn changes heading at exactly 3 degrees per second, so a full 360 takes two minutes. It's the default turn rate in most instrument flight procedures.

Does altitude affect the rate of turn?

The formula uses gravitational acceleration, which decreases slightly with altitude. At typical flight altitudes below 40,000 feet, this effect is negligible (less than 0.5%).

What's the difference between rate of turn and radius of turn?

Rate of turn measures how fast the heading changes (degrees per second). Radius of turn measures how large the circular path is (meters or feet). They're inversely related: a higher turn rate means a tighter, smaller turn radius.

Can the bank angle exceed 60 degrees?

Technically yes, but bank angles above 60 degrees produce extreme load factors (2g or more) and are not used in normal operations. The calculator works up to just under 90 degrees, where the turn rate approaches infinity.

Why do faster aircraft need steeper banks for the same turn rate?

At higher speeds, the aircraft covers more distance per second. To change direction at the same angular rate, more centripetal force is needed, which means tilting the lift vector further from vertical with a steeper bank angle.