Enter the velocity of object A relative to object B, and the velocity of object B relative to object C, to determine the relative velocity of A relative to C.

Relative Velocity Calculator

1D (Colinear) 2D (Magnitude + Angle)

Enter any 2 values to calculate the missing variable (use negative for opposite directions)

Relative Velocity Formula

The following formula is used to calculate a relative velocity (classical/Galilean addition). In 1D, use a consistent sign convention (e.g., right/east is positive). In 2D/3D, treat each velocity as a vector.

Vac = Vab + Vbc
  • Where Vac is the velocity of A relative to C (A with respect to C).
  • Vab is the velocity of A relative to B (A with respect to B).
  • Vbc is the velocity of B relative to C (B with respect to C).

To calculate a relative velocity from A to C, add the relative velocity from A to B and the relative velocity from B to C (with consistent directions/angles). For speeds close to the speed of light, use relativistic velocity addition instead.

Relative Velocity Definition

Relative velocity is the velocity of one object measured in the reference frame of another object (equivalently, the difference between their velocity vectors in a chosen inertial frame).

Relative Velocity Example

How to calculate a relative velocity?

  1. First, determine the velocity of A relative to B.

    Calculate the velocity of A relative to B.

  2. Next, determine the velocity of B relative to C.

    Measure the velocity of B relative to C.

  3. Finally, calculate the velocity of A relative to C.

    Calculate the velocity of A relative to C using the equation above (with a consistent sign convention in 1D, or vector directions/angles in 2D).

FAQ

What is a relative velocity?

A relative velocity is the velocity of an object when measured in the reference frame of another object. For example, if object A is moving at 10 m/s relative to the ground and object B is moving at 5 m/s relative to the ground in the same direction, then the velocity of A relative to B is 10 − 5 = 5 m/s (in that direction). If they move in opposite directions, the relative speed would be 15 m/s.