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Resultant Velocity Calculator — result sheet
Combine perpendicular velocity components to find resultant speed, horizontal direction, and elevation angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Resultant magnitude = √(vx² + vy² + vz²); horizontal direction = atan2(vy, vx).
Velocity is a vector, so perpendicular components must be combined with both magnitude and direction retained. This tool handles two-dimensional motion and an optional vertical component, which is useful for wind addition, navigation, robotics, and introductory kinematics when the coordinate axes are defined clearly.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X-component velocity — velocity units; minimum -1000000000; maximum 1000000000
- Y-component velocity — velocity units; minimum -1000000000; maximum 1000000000
- Z-component velocity — velocity units; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| X-component velocity | 30 |
| Y-component velocity | 40 |
| Z-component velocity | 0 |
The resultant speed is 50 velocity units and the horizontal direction is about 53.13° from +X.
Assumptions and limits
- The three components are perpendicular and use the same velocity unit and reference frame.
- The horizontal direction is measured counterclockwise from the positive x-axis and wrapped to 0–360 degrees.
- The result is vector arithmetic only; it does not model acceleration, drag, terrain, relativistic effects, or a changing reference frame.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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