How the Angle of Attack Calculator Works
The angle of attack, often written as α or AoA, is the angle between an airfoil chord line and the incoming relative airflow.
In a simplified velocity-component model, the angle can be estimated using the vertical and forward velocity components:
where Vz is the vertical velocity component and Vx is the forward velocity component.
Angle of Attack Formula
The calculator uses atan2 rather than simple arctan because atan2 handles signs and quadrants more safely.
Example Calculation
Vertical velocity Vz = 5 m/s Forward velocity Vx = 50 m/s Chord offset = 0 degrees
The angle is:
Angle of Attack vs Pitch Angle
| Term | Meaning |
|---|---|
| Angle of attack | Angle between chord line and relative airflow. |
| Pitch angle | Aircraft nose attitude relative to the horizon. |
| Flight path angle | Aircraft trajectory angle relative to the horizon. |
Why Angle of Attack Matters
Angle of attack affects lift, drag, flow separation, and stall behavior. Increasing AoA usually increases lift up to a point, but after the critical angle, the wing can stall.
Frequently Asked Questions
Is AoA the same as climb angle?
No. A climb angle describes the aircraft path relative to the horizon. AoA describes the angle between the wing chord and the incoming airflow.
Can AoA be negative?
Yes. A negative AoA can occur when the vertical velocity component or relative airflow direction gives a negative angle relative to the chord reference.
Why use atan2 instead of arctan?
atan2 handles positive and negative velocity components better and avoids division-by-zero problems when the forward velocity is zero.
Can this predict stall?
No. Stall depends on the aircraft, wing, Reynolds number, Mach number, flap configuration, contamination, turbulence, and many other conditions.