Resultant Velocity Calculator

Enter two velocity vectors (by magnitude & angle, or by components) into the calculator to determine the resultant velocity.

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Resultant Velocity Formula

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

V_m=\sqrt{\left(\sum_i V_{x i}\right)^2+\left(\sum_i V_{y i}\right)^2}

• Where V_m is the resultant velocity magnitude
• V_xi are the x-components of each velocity vector
• V_yi 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.

V_a = Tan^-1 (V_y/V_x)

• Where V_a is the angle (direction) of the resultant velocity
• V_x is the x-component of the resultant velocity
• V_y is the y-component of the resultant velocity

Note: to get the correct quadrant for the direction, it’s best to compute the angle using atan2(V_y, V_x) rather than using only Tan^-1(V_y/V_x).

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.

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