Angle of Attack Calculator

Estimate angle of attack from forward and vertical velocity components using the atan2 function.

Aviation safety note: This calculator is for educational aerodynamic estimation only. Do not use it for real flight operations, flight planning, aircraft control, certification, or safety decisions.

About the Author: Created by Fotios Angelakis, MSc in Mechanical Engineering, with experience in aerodynamics, engineering calculations, and applied calculator tools. Learn more about the author's qualifications and experience.

Enter velocity components and click calculate.

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:

α = atan2(Vz, Vx)

where Vz is the vertical velocity component and Vx is the forward velocity component.

relative airflow chord line α Angle between chord line and relative airflow

Angle of Attack Formula

AoA = atan2(vertical velocity, forward velocity)

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:

α = atan2(5, 50) = 5.71°

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.

Safety reminder: Real aircraft AoA depends on aircraft attitude, wing geometry, local airflow, sensor position, calibration, sideslip, flap configuration, turbulence, and flight condition. This page is not a cockpit instrument.

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.