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🧮 Resultant Velocity Calculator

Calculate the resultant speed and direction when combining two velocity vectors, like an aircraft’s airspeed with wind, or a boat with a current.

First Velocity Magnitude

m/s

First Velocity Direction

deg

Second Velocity Magnitude

m/s

Second Velocity Direction

deg

What resultant velocity is

When two velocities act on an object at the same time — like an aircraft’s airspeed and a crosswind, or a swimmer’s stroke and a river current — the resultant velocity is the single combined velocity vector that represents both effects together.

The formula

Each velocity is broken into x and y components using v_x = v·cos(θ) and v_y = v·sin(θ). The components from both vectors are added together, and the resultant magnitude is √(x² + y²), with direction θ = atan2(y, x).

This is standard vector addition, applicable to any two-dimensional combination of velocities (or other vector quantities like forces or displacements).

Last reviewed August 2026