Magnitude of Acceleration Calculator

Use our magnitude of acceleration calculator to find magnitude for an acceleration vector.

Acceleration Vector Type:

Magnitude of Acceleration:


Magnitude of Acceleration Formula

\left| \vec{a} \right| = \sqrt{a_{x}^{2} + a_{y}^{2}}
Learn how we calculated this below

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How to Calculate the Magnitude of Acceleration

Acceleration describes how quickly an object changes its velocity over time, and is composed of the direction of the change in velocity along with the magnitude.

Acceleration is a vector quantity, which means it has both a magnitude and a direction. The SI unit for acceleration is meters per second squared (m/s²).

Note that the basic formula to calculate acceleration a is:

a= \frac{\Delta v}{\Delta t}

Δv = change in velocity
Δt = change in time

To find the magnitude of acceleration, you need to consider the components of velocity change in a coordinate system (usually Cartesian coordinates with x, y, and z axes). You can find the magnitude of acceleration in a few steps:

Step 1 – Determine the Components of Velocity Change: Calculate the change in velocity components (Δvx, Δvy, Δvz) along each axis over the time interval Δt.

Step 2 – Apply the Acceleration Formula for Each Component:

  • ax = Δvx / Δt
  • ay = Δvy / Δt
  • az = Δvz / Δt

Step 3 – Calculate the Magnitude of Acceleration: Use the Pythagorean theorem in three dimensions to find the total magnitude of the acceleration vector from its components:

\left| \vec{a} \right| = \sqrt{a_{x}^{2} + a_{y}^{2} + a_{z}^{2}}

This formula results from the vector addition of the acceleration components and gives the overall magnitude of acceleration regardless of direction.

How to Calculate the Magnitude Using the Mass of an Object and Force

You can also calculate the acceleration magnitude if you know the mass of an object and the force acting on it. Newton’s second law of motion states that the force acting on an object is equal to the product of its mass and acceleration.

Using this law, you can find the magnitude of acceleration using the formula:

\left| a \right| = \left| \frac{F}{m} \right|

F = net force
m = mass

Thus, the magnitude of acceleration is equal to the net force acting on an object divided by the object’s mass.