Resultant Velocity Calculator

The resultant velocity calculator allows you to add up to five different velocity vectors, determining the absolute value of the resultant velocity, its direction, and its x and y components.

Resultant magnitude36.682109from components 17.0096, 32.5

Direction62.3737°anticlockwise from the positive x axis

x component17.009619

y component32.5

Sum of magnitudes85the resultant equals this only when every vector points the same way — otherwise it is smaller

Vector 1: 30 at 0°30, 0x, y components

Vector 2: 40 at 90°0, 40x, y components

Vector 3: 15 at 210°-12.9904, -7.5x, y components

Equilibrant36.682109 at 242.3737°the single vector that would cancel the resultant and bring the system into equilibrium

The formula

resultant = √(Σx² + Σy²), direction = atan2(Σy, Σx)

Components first, always

Vectors cannot be added by adding magnitudes. Two 30-newton forces sum to 60 N if they point the same way, to zero if they oppose, and to 42.4 N at right angles. The reliable method is always the same: resolve each vector into x and y components, add the components separately, then recombine.

Use atan2 rather than atan for the direction. A plain arctangent of y over x cannot distinguish a resultant pointing down-left from one pointing up-right, because dividing two negatives gives a positive — atan2 keeps both signs and returns the correct quadrant.

The equilibrant is the resultant reversed. It is what you would have to add to bring the system to equilibrium, which makes it the useful answer in statics problems where the question is what force holds something still.