Velocity Calculator
Velocity is a vector quantity that describes both the speed and direction of an object's motion. When motion occurs in two dimensions, you can decompose velocity into horizontal (vx) and vertical (vy) components. This calculator finds the resultant velocity magnitude and direction from those components using the Pythagorean theorem and inverse tangent.
The resultant velocity is found using v = √(vx² + vy²), which is the Pythagorean theorem applied to the velocity vector. The direction angle is calculated with θ = atan2(vy, vx), giving the angle measured counterclockwise from the positive x-axis.
Understanding velocity components is essential for analyzing projectile motion, navigation, and any two-dimensional motion problem. For example, a ball thrown at an angle has a constant horizontal velocity (ignoring air resistance) and a changing vertical velocity due to gravity. By resolving these components, you can predict the trajectory of the ball.
Unlike speed, which is a scalar and always positive, velocity can have negative components indicating direction. A negative vx means motion to the left, while a negative vy means downward motion. The direction angle fully captures this directional information in a single value between -180° and 180°.