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Relative Velocity Calculator

Work out relative velocity instantly with clear inputs, formula shown and shareable results.

About Relative Velocity Calculator

Relative velocity is a vector subtraction, so its magnitude follows the cosine rule: sqrt(va^2 + vb^2 - 2.va.vb.cos theta). At 90 degrees the cosine term vanishes and 30 m/s against 20 m/s gives 36.06 m/s. Head-on the speeds add to 50 m/s; travelling together they subtract to 10 m/s.

Formulas

Cosine rule for relative speed

v(rel) = sqrt(vA^2 + vB^2 - 2 vA vB cos theta)

Limiting cases

head-on: vA + vB; same direction: |vA - vB|

Worked example

With the default values below, Relative Velocity Calculator returns Relative Speed Of A With Respect To B of 36.056. Change any input above and every figure here is recalculated in your browser.

Inputs used

Speed of object Aminimum 0 m/s
30 m/s
Speed of object Bminimum 0 m/s
20 m/s
Angle between their directionsaccepts 0–180 deg
90 deg

Results

Relative Speed Of A With Respect To B
36.056 m/s
Closing Rate Along A's Line
30.000 m/s
Relative Speed If Head-On
50.000 m/s
Relative Speed If Travelling Together
10.000 m/s

Step by step

  1. 1Values used
  2. 2Cosine rule for relative speed
  3. 3Limiting cases
  4. 4Relative Speed Of A With Respect To B= 36.056 m/s
  5. 5Closing Rate Along A's Line= 30.000 m/s
  6. 6Relative Speed If Head-On= 50.000 m/s
  7. 7Relative Speed If Travelling Together= 10.000 m/s

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does the head-on case add?

Because at 180 degrees the cosine is -1, so the cross term becomes +2.vA.vB and the expression collapses to (vA + vB)^2.

Is relative velocity symmetric?

The magnitude is the same either way round; the direction reverses. A relative to B is the negative of B relative to A.

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