Magnitude of Acceleration Calculator
Enter the x, y, and z components of an acceleration vector to calculate its total magnitude and direction angle.
Finding the magnitude of a vector
Acceleration is a vector quantity, meaning it has both size and direction. When acceleration acts along multiple axes at once (as measured by an accelerometer, for example), the overall magnitude combines all components.
The formula
The magnitude of a 3D acceleration vector is found using the Pythagorean theorem extended to three dimensions: |a| = √(ax2 + ay2 + az2). The calculator also reports the direction angle within the XY-plane using the arctangent of ay ÷ ax.
This calculation works for any orthogonal (perpendicular) set of component axes; leave the Z-component at zero for a purely 2D vector problem. This calculator is for general physics and engineering education.