Calculate degrees per second, turn radius, and load factor based on airspeed and bank angle.
Enter speed in Knots (KTAS).
Enter angle of bank in Degrees (°).
Rate of Turn:— deg/sec
Turn Radius:— ft
Diameter of Turn:— NM
Time for 360° Turn:— min:sec
Load Factor (G):— G
How to Calculate Turn Rate in Aviation
In aerodynamics and flight mechanics, the Turn Rate (or Rate of Turn) determines how many degrees of heading an aircraft changes per second. This calculation is critical for pilots executing Standard Rate Turns (3 degrees per second) during instrument flight rules (IFR) operations and holding patterns.
The Physics Formulas
The turn performance of an aircraft is derived from the relationship between the horizontal lift component and the aircraft's velocity. We use the following formulas:
Rate of Turn (ROT):ROT = (1,091 × tan(Bank Angle)) / True Airspeed. The result is in degrees per second.
Radius of Turn:Radius = (True Airspeed²) / (11.26 × tan(Bank Angle)). This provides the radius in feet.
Load Factor (G-Force):G = 1 / cos(Bank Angle). This represents the additional force felt by the pilot and airframe during a level turn.
Understanding the Variables
When calculating turn rate, two primary variables affect the outcome:
True Airspeed (TAS): As speed increases, the radius of the turn increases, and the rate of turn decreases for a specific bank angle. To maintain a standard rate turn at higher speeds, the bank angle must be increased.
Bank Angle: A steeper bank increases the horizontal component of lift, which pulls the aircraft into the turn tighter and faster. However, this also exponentially increases the Load Factor (G-force).
Standard Rate Turn Example
A "Standard Rate Turn" is defined as 3° per second, completing a full 360° circle in exactly 2 minutes (120 seconds). A common rule of thumb to estimate the required bank angle for a standard rate turn is (Airspeed in Knots / 10) + 7.
function calculateTurnPhysics() {
// 1. Get input values
var tasInput = document.getElementById("trueAirspeed");
var bankInput = document.getElementById("bankAngle");
var resultDiv = document.getElementById("trResultContainer");
// 2. Parse values
var tas = parseFloat(tasInput.value);
var bankDeg = parseFloat(bankInput.value);
// 3. Validation
if (isNaN(tas) || tas <= 0) {
alert("Please enter a valid positive True Airspeed.");
return;
}
if (isNaN(bankDeg) || bankDeg = 90) {
alert("Please enter a valid Bank Angle between 0 and 90 degrees.");
return;
}
// 4. Mathematical Logic
// Convert degrees to radians for JS Math functions
var bankRad = bankDeg * (Math.PI / 180);
// Formula: Rate of Turn (deg/sec) = (1091 * tan(theta)) / TAS
var rateOfTurn = (1091 * Math.tan(bankRad)) / tas;
// Formula: Radius (ft) = (TAS^2) / (11.26 * tan(theta))
var radiusFt = (tas * tas) / (11.26 * Math.tan(bankRad));
// Convert Radius to Nautical Miles (1 NM = 6076.12 ft)
var radiusNM = radiusFt / 6076.12;
var diameterNM = radiusNM * 2;
// Formula: Time for 360 turn (seconds) = 360 / Rate
var timeSeconds = 360 / rateOfTurn;
// Format time into MM:SS
var mins = Math.floor(timeSeconds / 60);
var secs = Math.round(timeSeconds % 60);
var formattedTime = mins + " min " + (secs 5280) {
// Show miles if very large
var sm = radiusFt / 5280;
document.getElementById("resRadius").innerText = radiusFt.toLocaleString("en-US", {maximumFractionDigits: 0}) + " ft (" + sm.toFixed(2) + " SM)";
} else {
document.getElementById("resRadius").innerText = radiusFt.toLocaleString("en-US", {maximumFractionDigits: 0}) + " ft";
}
document.getElementById("resDiameter").innerText = diameterNM.toFixed(2) + " NM";
document.getElementById("resTime360").innerText = formattedTime;
document.getElementById("resGforce").innerText = loadFactor.toFixed(2) + " G";
// Show results
resultDiv.style.display = "block";
}