Vector Acceleration Calculator

x-component of acceleration (m/s^2):

y-component of acceleration (m/s^2):

Calculate

Results

Magnitude of Acceleration (A): 0 m/s^2
Angle of the Acceleration Vector (α): 0 degrees

 

About Vector Acceleration Calculator (Formula)

Acceleration is a vector quantity, meaning it has both magnitude (size) and direction. The magnitude (or length) of the acceleration vector can be determined using the Pythagorean theorem:

A=SQRT(Ax2+Ay2)

Where:

• $A$ represents the magnitude of the acceleration.
• $Ax$ and $Ay$ are the x and y components of the acceleration vector, respectively.

This formula calculates the length (or magnitude) of the acceleration vector in a two-dimensional plane. Essentially, you’re finding the length of the hypotenuse in a right triangle where $Ax$ and $Ay$ are the two shorter sides.

2. Angle of the Acceleration Vector:

To understand the direction in which the acceleration is acting, we can calculate the angle $\alpha$ that the acceleration vector makes with the positive x-axis:

Where:

• tan−1 is the arctangent (or inverse tangent) function.
• $Ay$ is the y-component of acceleration.
• $Ax$ is the x-component of acceleration.

This formula gives the angle in radians. To convert it to degrees, you typically multiply by 180π180​.

The use of the arctangent function ensures that the resulting angle is in the correct quadrant, as tan−1 takes into account the signs of both components $Ax$ and $Ay$.