Calculate the magnitude and direction of the resultant velocity from two perpendicular velocity components.
Last updated: March 2026 | By ForgeCalc Engineering
Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. When an object is moving in two directions simultaneously (like a boat crossing a river), its overall or "resultant" velocity is the vector sum of its individual components.
The magnitude of the resultant velocity is calculated using the Pythagorean theorem, and the direction is found using trigonometry (the arctangent function). This is fundamental in navigation, projectile motion, and fluid dynamics.
Where:
• v is the resultant velocity magnitude
• θ is the angle relative to the horizontal
• v_x is the horizontal component
• v_y is the vertical component
A vector is a quantity that has both magnitude and direction. Examples include velocity, force, and displacement. Speed, on the other hand, is a scalar (magnitude only).
For velocities at any angle, you first break each velocity into its own x and y components using sine and cosine, sum all x-components and all y-components, and then use this calculator on the totals.
Relative velocity is the velocity of an object as observed from another moving object. For example, if you are walking at 5 km/h on a train moving at 100 km/h, your resultant velocity relative to the ground is 105 km/h.
The arctan2 function handles all four quadrants correctly, taking into account the signs of both v_x and v_y to determine the true angle from 0 to 360 degrees.
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