How this calculator works
Convert every planar velocity into Cartesian components before adding. Adding scalar speeds is valid only when all vectors point in the same direction. The result magnitude comes from the component norm and its direction comes from the two-argument arctangent. A zero vector has no direction; the calculator states that explicitly. All velocities must describe compatible relative motions in one coordinate system.
Formula
Vx=sum(vi cos(theta_i)); Vy=sum(vi sin(theta_i)); |V|=sqrt(Vx^2+Vy^2); theta=atan2(Vy,Vx).
Worked example
A 3 m/s vector along x plus a 4 m/s vector along y gives (3,4) m/s, speed 5 m/s and direction 53.130102 degrees. Two opposite 3 m/s vectors cancel.
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Frequently asked questions
Are these compass bearings?
No. Zero is the positive x-axis and positive angles turn counterclockwise. Use the ground-speed calculator for compass bearings.
Why is the resultant smaller than the sum of speeds?
Components pointing in opposite directions partially cancel.
Can I enter more than two vectors?
Yes. Choose three, four or five. Only the selected vectors participate in the calculation.