How to Calculate Pivotal Altitude: Formula, Chart & Calculator
Pivotal altitude is the height at which a selected ground reference appears to remain fixed relative to a point on the wing while the airplane turns around it. It is a key concept in eights on pylons, and the number changes with groundspeed.
How to calculate pivotal altitude
For the common knots-and-feet rule, square the groundspeed in knots and divide by 11.3. At 100 knots groundspeed, 100² ÷ 11.3 gives about 885 feet AGL. At 120 knots, 120² ÷ 11.3 gives about 1,274 feet AGL.
The formula is a training rule of thumb. The FAA Airplane Flying Handbook uses the same relationship and explains that the computed height is referenced to the ground. If you need an MSL altitude for situational awareness, add the elevation of the area around the pylon to the calculated AGL height.
Where does the 11.3 come from?
The knots-and-feet shortcut is not an arbitrary memorization constant. In a coordinated level turn, turn radius is R = V² ÷ (g × tan φ). The pylon geometry gives h = R × tan φ. Substitute the turn-radius equation into the geometry and the bank-angle term cancels:
That equation uses consistent physical units. Convert groundspeed from knots to feet per second and use standard gravity, and the constant works out to about 0.0885 feet per knot squared. The reciprocal is about 11.3, giving the familiar training shortcut:
This cancellation is also why bank angle does not appear as a separate input in the basic pivotal-altitude formula. Bank changes the turn radius needed for the geometry, but the corresponding sight-line geometry changes with it.
Pivotal altitude chart
This quick chart uses groundspeed in knots and the GS² ÷ 11.3 relationship. Values are rounded to the nearest foot.
| Groundspeed | Approx. pivotal altitude |
|---|---|
| 70 kt | 434 ft AGL |
| 80 kt | 566 ft AGL |
| 90 kt | 717 ft AGL |
| 100 kt | 885 ft AGL |
| 110 kt | 1,071 ft AGL |
| 120 kt | 1,274 ft AGL |
| 130 kt | 1,496 ft AGL |
| 140 kt | 1,735 ft AGL |
The important pattern is not the individual number. Because groundspeed is squared, a relatively small increase in groundspeed produces a much larger increase in pivotal altitude.
Why pivotal altitude changes during eights on pylons
Wind changes the airplane's groundspeed as it moves around the pylons. On the faster, downwind portion of the maneuver, pivotal altitude increases. On the slower, upwind portion, pivotal altitude decreases. That is why eights on pylons are not normally flown by selecting one altitude and trying to hold it all the way around.
The visual picture drives the maneuver. The FAA Airplane Flying Handbook, Chapter 7, describes the correction relative to the wing reference: if the pylon appears to move ahead, decrease altitude; if the pylon appears to move behind, increase altitude. Keep the rudder for coordination rather than yawing the reference line onto the pylon. Practice the maneuver with an instructor using the current ACS and aircraft procedures.
Use groundspeed, not indicated airspeed
One of the most common errors is plugging indicated airspeed into the formula. Pivotal altitude is tied to how fast the airplane is moving over the ground, so groundspeed is the required input. A constant indicated airspeed in wind can still produce a changing groundspeed and therefore a changing pivotal altitude.
Does bank angle change pivotal altitude?
Not directly. The basic relationship depends on groundspeed, not bank angle. Bank is adjusted to maintain the desired pylon geometry and ground track. If a steeper bank or another maneuvering change alters groundspeed, then the pivotal altitude changes because the groundspeed changed—not because bank angle appears as a separate term in the formula.
Pivotal altitude in MPH
If groundspeed is expressed in miles per hour instead of knots, do not use 11.3. With groundspeed in MPH, the FAA training divisor is 15: pivotal height in feet ≈ MPH² ÷ 15. Keeping the units attached to the formula is important because using the knots constant with MPH produces a wrong answer.
Quick checkride examples
Example 1: 90 knots groundspeed gives about 717 feet AGL. Example 2: 110 knots gives about 1,071 feet AGL. Example 3: a change from 100 to 120 knots does not increase pivotal altitude by 20 percent; because the speed is squared, the altitude rises from about 885 to 1,274 feet, roughly a 44 percent increase.
Pivotal altitude questions
How do you calculate pivotal altitude?
With groundspeed in knots, square the groundspeed and divide by 11.3. The answer is an approximate height in feet AGL.
Is pivotal altitude AGL or MSL?
The formula gives height above the ground reference. Add the local ground elevation if you need to compare that height with an MSL altitude.
Why does wind matter?
Wind changes groundspeed around the maneuver. Higher groundspeed requires a higher pivotal altitude; lower groundspeed requires a lower one.
Is pivotal altitude only used for eights on pylons?
It is most commonly taught in connection with eights on pylons because that commercial maneuver makes the pivotal relationship visually obvious.
Where does 11.3 come from?
Start with h = V²/g, convert knots to feet per second, and use standard gravity. The unit conversion produces the familiar knots-and-feet approximation GS² ÷ 11.3.
Related PilotDesk tools
Pivotal Altitude Calculator · Pilot Checkride Math · Aircraft Performance Reference · Turn Radius Calculator · Rate of Turn Calculator
Source check
The FAA Airplane Flying Handbook explains pivotal altitude and gives the groundspeed-squared rule of thumb. See the FAA Airplane Flying Handbook and PilotDesk Sources & Methods.