Relative Velocity Calculator (1D)
Combine two one-dimensional velocities to find how fast one object moves as seen from the other, and whether they close or separate.
How it works
v(A relative to B) = v_A − v_B · v(B relative to A) = v_B − v_A · relative speed = |v_A − v_B|
Relative velocity in one dimension is just the vector difference of the two velocities along the line. Working in B’s frame you subtract B’s velocity from everything, so A appears to move at v_A − v_B. When the objects head toward each other their signed velocities have opposite signs, and the subtraction adds their speeds — which is why two cars approaching at 30 and 20 m/s close at 50 m/s.
Worked example
A moves right at +10 m/s and B moves left at −5 m/s. Velocity of A relative to B = 10 − (−5) = +15 m/s, so from B’s seat A rushes past at 15 m/s. Velocity of B relative to A = −5 − 10 = −15 m/s, the same speed the other way.
Sources: Relative velocity — Wikipedia
Frequently asked questions
Why do closing speeds add up?
When two objects move toward each other their velocities have opposite signs. Subtracting a negative velocity is the same as adding, so v_A − v_B becomes the sum of the two speeds — the rate at which the gap shrinks.
How do I set the signs?
Pick one direction along the line as positive. Any velocity in that direction is positive; anything the other way is negative. The calculator then handles the arithmetic consistently.
What is the difference between relative velocity and relative speed?
Relative velocity keeps a sign showing direction (v_A − v_B), while relative speed is its magnitude |v_A − v_B|. The speed tells you how fast the two separate or approach; the sign tells you which.
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This calculator is for educational purposes. Double-check important results before acting on them.