Calculate vertical acceleration from vector components, forces and mass, or velocity change over time, with results in g's and m/s², ft/s², or in/s².

Upward is positive. Vector angles are measured counterclockwise from the positive horizontal axis. Forces include gravity; velocity change gives average acceleration.

Positive angles point above the rightward horizontal axis; negative angles point below it.

Vertical Acceleration Formula

The following equation is used to calculate the Vertical Acceleration.

Ay = At × SIN (a)
  • Where Ay is the Vertical Acceleration (m/s^2)
  • At is the total acceleration (m/s^2)
  • a is the angle of the acceleration vector measured from the positive horizontal axis (degrees); upward is positive

To calculate the signed vertical acceleration, multiply the nonnegative total magnitude by the sine of the angle measured from horizontal. For an angle inferred from the vertical component alone, the principal arcsine direction and its supplementary direction are both possible. In the force mode, ay = (upward applied force − additional downward force) / mass − gravity; weight is counted separately once. The velocity mode gives average ay = (final vertical velocity − initial vertical velocity) / elapsed time.

What are the units for Vertical Acceleration?

In the International System of Units, also known as SI units, the units for Vertical Acceleration are m/s^2.

How to Calculate Vertical Acceleration?

Example Problem:

The following example problem outlines the steps and information needed to calculate the Vertical Acceleration.

First, determine the total acceleration. In this example, the total acceleration is calculated or measured to be 100 (m/s^2).

Next, determine the angle of the acceleration vector. For this problem, the angle of the acceleration vector is determined to be 20 (degrees).

Finally, calculate the Vertical Acceleration using the formula above: 

Ay = At * SIN ( a) 

Inserting the values from above and solving the equation with the imputed values gives: 

Ay = 100* SIN ( 20deg)  = 34.202 (m/s^2)