Relative Velocity Calculator
Enter object speed v_A and observer speed v_B to compute relative velocity v'=v_A−v_B and closing speed |v_A−v_B|. Same direction subtracts, opposite adds. Two cars at 50 and −50 km/h → closing 100 km/h.
Input Data
Results
At a glance:Relative velocity is a core kinematics concept: the velocity of object A relative to observer B is v_AB=v_A−v_B. The Galilean transformation (1632) applies in low-speed (v≪c) inertial frames. Same-direction motion subtracts, opposite-direction adds. Physical meaning: velocity is relative, depending on the reference frame. On the ground a car at 50 km/h has a different relative speed to an observer co-rotating with Earth. Inertial frames are equivalent: you cannot tell uniform motion from rest by a mechanics experiment (Galilean relativity). The closing speed takes the absolute value, used for meeting, pursuit and collision analysis. Applications: (1) traffic meeting (two cars head-on add); (2) ship sailing (current+ship speed); (3) aircraft landing (ground speed=airspeed+wind); (4) sports racing (relay, pursuit); (5) pursuit problems (when to catch up). Limit: fails near light speed, where relativistic velocity addition is needed.
Formula
Relative velocity: v' = v_A − v_B
Closing speed: v_close = |v_A − v_B|
Galilean transform: x' = x − v_B·t
1-D velocity composition: v' = v_A − v_B
$$v_{AB} = v_A - v_B, \quad v_{close} = |v_A - v_B|$$How to Use
- Enter object velocity v_A (m/s).
- Enter observer velocity v_B (m/s); same direction +, opposite −.
- The tool gives relative velocity and closing speed.
Case Studies
Traffic meeting and aircraft landing
Two cars head-on: v_A=50, v_B=−50 km/h → v'=100 km/h. The impact equals hitting a wall at 100 km/h.
Aircraft: ground speed = airspeed + wind. Tailwind shortens the trip, headwind lengthens it.
Pursuit: a police car at 30 m/s chasing at 25 m/s closes at 5 m/s; to catch 100 m needs 20 s.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.