Relative Velocity Calculator

Calculate the relative velocity between two objects moving in different directions. This calculator helps you determine how one object’s motion appears from the perspective of another moving object.

How to Use This Calculator

1. Enter the first object’s velocity (speed and direction)
2. Enter the second object’s velocity
3. The calculator will determine their relative velocity

Understanding Relative Velocity

Relative velocity is the velocity of an object as observed from a reference frame in motion. It’s calculated by finding the vector difference between two velocities:

• If objects move in the same direction: Relative velocity = |v₁ - v₂|
• If objects move in opposite directions: Relative velocity = |v₁ + v₂|
• For objects moving at an angle: Relative velocity = √[(v₁)² + (v₂)² - 2v₁v₂cos(θ)]

where:

• v₁ is the velocity of the first object
• v₂ is the velocity of the second object
• θ is the angle between their velocity vectors

Common Applications

1. Traffic Analysis

   • Calculating closing speeds between vehicles
   • Determining safe passing distances

2. Aviation

   • Computing aircraft approach speeds
   • Planning intercept courses

3. Physics Education

   • Solving motion problems
   • Understanding reference frames

4. Maritime Navigation

   • Ship collision avoidance
   • Course plotting

Tips for Accurate Calculations

• Always use consistent units (all speeds in m/s or km/h)
• Consider the direction of motion carefully
• For angles, use degrees measured from a common reference direction
• Remember that relative velocity is always measured from one object’s perspective

Technical Notes

• The calculator handles both one-dimensional and two-dimensional relative motion
• Results are provided in multiple common units for convenience
• Calculations account for both magnitude and direction of motion