Relative Velocity Calculator

Use this relative velocity calculator to find how fast one object appears to move from the perspective of another. Enter the First object speed, Second object speed, Angle between velocities, and Speed unit to get the relative velocity magnitude.

How to use this calculator

1. Enter the non-negative speed of the first object.
2. Enter the non-negative speed of the second object.
3. Enter the angle between their velocity directions, from 0 to 360 degrees.
4. Choose meters per second, kilometers per hour, or miles per hour.

If you need a unit change before entering speeds, use the speed converter. For acceleration problems, see the acceleration converter.

Formula

$relative\ velocity = \sqrt{v_1^2 + v_2^2 - 2v_1v_2\cos\theta}$

This vector formula returns the magnitude of one velocity relative to the other.

Worked example

Suppose object one moves at 10 m/s, object two moves at 5 m/s, and the angle between them is 60 degrees.

$\sqrt{10^2 + 5^2 - 2 \times 10 \times 5 \times \cos 60^\circ} = 8.66$

The relative velocity is 8.66 m/s.

Interpreting directions

An angle of 0 degrees means both velocities point the same way, so only the speed difference remains. An angle of 180 degrees means opposite directions, so speeds add as a closing speed. For motion measured in feet per second, the feet per second to meters per second calculator can prepare inputs.