Calculate the resultant velocity of two vectors from magnitudes and angles or x/y components, with direction and X/Y components shown.

Angles run counterclockwise from +x. Use the same axes for both vectors; this is ordinary nonrelativistic vector addition.

Resultant Velocity Formula

The following formula is used to calculate a resultant velocity magnitude from component sums.

Vₘ = √((Σᵢ Vx i)² + (Σᵢ Vy i)²)
  • Where Vm is the resultant velocity magnitude
  • Vxi are the x-components of each velocity vector
  • Vyi are the y-components of each velocity vector

To calculate the magnitude of the resultant velocity, add together all of the x-component values and square the result. Do the same for the y-components, then add this to the previous value. Finally, take the square root of that result to get the magnitude.

Va = atan2(Vy, Vx), normalized to 0° ≤ Va < 360°. Direction is undefined when both resultant components are zero.

  • Where Va is the angle (direction) of the resultant velocity
  • Vx is the x-component of the resultant velocity
  • Vy is the y-component of the resultant velocity

Angles are measured counterclockwise from the positive x-axis. Use the same coordinate axes for both vectors. The calculator uses ordinary nonrelativistic vector addition; for relative motion, combine compatible velocities such as boat relative to water plus water relative to shore.

Resultant Velocity Definition

A resultant velocity is the single velocity vector that is equivalent to the vector sum of two or more velocities in different directions.

Is resultant velocity the same as final velocity?

Not necessarily. In this context, “resultant” (or “net”) velocity means the vector sum of the velocities you are combining at a given instant or for a defined situation. “Final velocity” usually refers to the velocity after a time interval of motion (often involving acceleration), so it depends on the dynamics and may not equal the resultant velocity.

How to calculate resultant velocity?

To calculate the resultant velocity, represent each velocity as a vector (magnitude and direction). Then break down each velocity into x and y components. Next, add together all of the x components and add together all of the y components. From these final x and y components, calculate the magnitude and direction of the resultant velocity.

FAQ

What is a resultant velocity?

A resultant velocity is the net (resultant) velocity vector from combining two or more velocities of given magnitudes and directions.