Relative Velocity Calculator

How it works

1. 1Enter the speed of each object and select whether they move in the same or opposite directions.
2. 2For same-direction motion the calculator subtracts: v_rel = v₁ − v₂; for opposite directions it adds: v_rel = v₁ + v₂.
3. 3The result is shown as a magnitude with a note indicating which object is faster or whether they are approaching.

Use cases

• Two cars on a highway: one at 30 m/s overtaking another at 20 m/s has a relative speed of 10 m/s.
• Aviation: a plane at 250 m/s into a 30 m/s headwind has an effective ground speed of 220 m/s.
• Sports: timing how quickly a runner at 8 m/s closes on a competitor at 6 m/s (2 m/s relative).

Frequently asked questions

Why subtract speeds for same-direction motion but add for opposite?

Relative velocity is the velocity of one object seen from the other’s frame. When both move the same way the observer keeps up with part of the motion, so the difference remains: v_rel = v₁ − v₂. When they move toward each other both contributions close the gap, so they add: v_rel = v₁ + v₂.

What does a negative result mean?

In the same-direction case, a negative result means object 2 is faster and is pulling away from object 1. The calculator shows the magnitude and explains the direction in a note below the result.

Can you show a worked example?

Car A travels at 30 m/s and Car B at 20 m/s. Same direction: 30 − 20 = 10 m/s (A gains 10 m every second on B). Opposite directions: 30 + 20 = 50 m/s (they close at 50 m/s, or 180 km/h).