Compute vector components from angles, points, or spatial inputs. Review magnitudes, direction angles, and coordinate changes with confidence.
| Method | Input | X Component | Y Component | Z Component |
|---|---|---|---|---|
| 2D Magnitude + Angle | Magnitude 12, Angle 35° | 9.830 | 6.883 | 0.000 |
| 2D Points | (2,3) to (8,11) | 6.000 | 8.000 | 0.000 |
| 3D Magnitude + Angles | Magnitude 15, Azimuth 40°, Elevation 25° | 10.422 | 8.745 | 6.339 |
| 3D Points | (1,2,3) to (6,9,12) | 5.000 | 7.000 | 9.000 |
Vector components split one vector into axis-based parts. In 2D, the horizontal part equals magnitude times cosine of the angle. The vertical part equals magnitude times sine of the angle.
2D formulas: x = r cos(θ), y = r sin(θ)
When you know two points, subtract the start coordinates from the end coordinates.
2D point formulas: x = x2 − x1, y = y2 − y1
For 3D inputs with azimuth and elevation, first resolve the vector in the xy-plane, then apply the vertical rise.
3D formulas: x = r cos(φ) cos(θ), y = r cos(φ) sin(θ), z = r sin(φ)
For 3D point inputs, subtract each start coordinate from its matching end coordinate.
3D point formulas: x = x2 − x1, y = y2 − y1, z = z2 − z1
The magnitude check is √(x² + y² + z²). Direction cosines are x/r, y/r, and z/r.
Choose the input method that matches your problem. Use the 2D angle option for plane vectors. Use the point options when you know start and end coordinates. Use the 3D angle option for spatial vectors with azimuth and elevation.
Enter the vector name if you want a labeled result. Add a unit if needed. Select degrees or radians for angular problems. Choose how many decimal places you want in the final result.
Press the button to calculate. The result appears above the form and below the header section. Review x, y, and z components, the magnitude check, quadrant, direction angles, and direction cosines. You can also export the result as CSV or PDF.
Vector components make large problems manageable. They break one vector into axis parts. That helps in algebra, geometry, mechanics, graphics, and navigation. Many equations become simpler after resolution into components. Signs also show direction clearly.
You can start with magnitude and angle. That is common in trigonometry. You can also use two points. That is useful in coordinate geometry. In spatial work, azimuth and elevation help describe direction in three dimensions.
A positive x component points right. A negative x component points left. A positive y component points up. A negative y component points down. In 3D, the z sign shows upward or downward direction along the third axis.
After finding the components, check the magnitude. Square each component. Add them. Then take the square root. The result should match the original vector length. This step helps confirm that the calculation is correct and complete.
Angle conventions matter. In 2D, angles are often measured from the positive x-axis. In 3D, azimuth is usually measured in the xy-plane. Elevation is measured above or below that plane. Always keep unit choice consistent.
This calculator supports classroom learning and fast checking. It works for coordinate questions, displacement problems, force resolution, and spatial modeling. It also helps when you need clean outputs for reports, practice sheets, or technical notes.
A vector component is the part of a vector along one axis. In 2D, vectors have x and y components. In 3D, they also have a z component.
Negative components show direction. They mean the vector points opposite to the positive axis direction. The size still comes from the numerical magnitude.
Yes. Select radians in the angle unit field. The calculator converts and applies the correct trigonometric values automatically.
Azimuth is the angle in the xy-plane. Elevation is the angle above or below the xy-plane. Together, they define many 3D directions.
Subtract the starting coordinates from the ending coordinates. This gives the directional change along each axis and forms the vector components.
The magnitude check confirms the result. It uses the component values to rebuild the vector length. Matching values improve confidence in the answer.
Direction cosines are ratios of each component to the vector magnitude. They describe how strongly the vector aligns with each axis.
Yes. A zero vector gives zero components and zero magnitude. Direction angles become non-informative because the vector has no direction.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.