Resultant Velocity Calculator

Velocity is a vector, which means it describes both how fast an object moves and the direction of that motion. When two motions act at the same time, their speeds cannot generally be added as ordinary numbers. They must be combined component by component. The resultant velocity calculator converts two magnitude-and-angle vectors into horizontal and vertical components, adds those components, and converts the sum back into a magnitude and direction. Angles are measured counterclockwise from the positive horizontal axis. Zero degrees points right, ninety degrees points up, one hundred eighty degrees points left, and negative ninety degrees points down. For each vector, the horizontal component equals magnitude times the cosine of its angle, while the vertical component equals magnitude times the sine. The resultant components are the sums of the corresponding inputs. Its magnitude follows from the Pythagorean theorem, and its direction comes from the two-argument arctangent so that the correct quadrant is retained. Vector addition is central to relative motion. A boat's velocity through water combines with a river current to produce its velocity over the ground. An aircraft's airspeed combines with wind velocity to determine ground speed and track. A person walking inside a moving vehicle has one velocity relative to the vehicle and another relative to the ground. The same method applies to displacement, acceleration, force, and other two-dimensional vectors even though this calculator labels results in meters per second. Signs and directions matter. Two equal vectors pointing the same way double the speed, while equal vectors in opposite directions cancel. Perpendicular vectors produce a magnitude found from their squared components, such as the familiar three-four-five triangle. Angles may be greater than three hundred sixty degrees or negative because sine and cosine repeat, although expressing a final bearing within a conventional range is often easier to interpret. This calculator assumes both velocities share the same reference frame, units, and coordinate axes. It performs ordinary Galilean vector addition, suitable for everyday mechanics where speeds are far below the speed of light. Relativistic velocity composition requires different equations. The tool also treats vectors as two-dimensional and does not include a vertical or z component beyond the displayed y-axis. Before using the answer, confirm the direction convention in your problem, convert all speeds to meters per second, and distinguish a mathematical angle from navigation bearings, which are commonly measured clockwise from north.