Magnitude of Acceleration Calculator

What Is the Magnitude of Acceleration?

When acceleration has components in multiple directions (such as horizontal and vertical), the magnitude gives the total acceleration — a single number representing the overall rate of change of velocity. This is calculated using the Pythagorean theorem applied to vectors.

How to Calculate Magnitude of Acceleration

Magnitude Formula

Where ax is the horizontal component and ay is the vertical component of acceleration, both in m/s².

The direction of the resultant acceleration vector is given by: θ = arctan(ay / ax).

Worked Example

A projectile has a horizontal acceleration of 0 m/s² and a vertical acceleration of −9.81 m/s² (gravity). The magnitude is:

|a| = √(0² + 9.81²) = 9.81 m/s²

For a car accelerating forward at 3 m/s² while turning with a centripetal acceleration of 4 m/s²:

|a| = √(3² + 4²) = √(9 + 16) = √25 = 5 m/s²

When to Use Magnitude of Acceleration

You need to find the magnitude whenever forces act in different directions simultaneously — such as projectile motion, banking turns, or objects on inclined planes. Use our net force calculator to find the resultant of multiple forces acting at different angles.