Result
Enter at least two vectorsCalculation details
Vector graph
The graph displays the x-y projection. Three-dimensional z-components remain available in the result and calculation steps.
Formula used
For Cartesian vectors, corresponding components combine independently: Rx = Σx, Ry = Σy, and Rz = Σz.
The resultant magnitude is |R| = √(Rx² + Ry² + Rz²). The two-dimensional direction is θ = atan2(Ry, Rx).
Polar inputs convert using x = r cos θ and y = r sin θ. Three-dimensional inputs also use horizontal magnitude r cos φ and z = r sin φ.
How to use
- Select two-dimensional or three-dimensional calculation.
- Choose addition, subtraction, or a linear combination.
- Add vectors and select each vector input format.
- Enter components, magnitude, direction, bearing, and coefficients.
- Select units, angle format, precision, and graph scale.
- Submit the form to view the full solution.
- Copy, export, print, share, or revisit saved history.
Example data
| Example | Vector A | Vector B | Expected resultant |
|---|---|---|---|
| 2D addition | (3, 4) | (-1, 6) | (2, 10) |
| 2D subtraction | (8, 3) | (2, -1) | (6, 4) |
| 3D addition | (2, -1, 4) | (5, 3, -2) | (7, 2, 2) |
| Polar addition | 5 at 0° | 5 at 90° | (5, 5) |
Recent calculation history
Frequently asked questions
What is vector addition?
Vector addition combines corresponding components. The result represents one equivalent vector. Its magnitude and direction describe the combined effect.
Can the calculator add more than two vectors?
Yes, you can add many vectors. Use the Add Vector button repeatedly. Every valid vector contributes to the final resultant.
Does it support three-dimensional vectors?
Yes, select the 3D option first. Each vector then includes a z-component. Elevation and three-dimensional magnitude are calculated automatically.
How are polar vectors converted?
The calculator resolves magnitude into components. Cosine produces the horizontal component. Sine produces the vertical component.
What happens when the resultant is zero?
A zero resultant has no defined direction. The calculator identifies cancelling vectors. Its unit vector also remains undefined.
Can I subtract vectors?
Yes, select the subtraction operation. The first vector remains positive. Every following vector is subtracted component-wise.
What is a linear combination?
A linear combination scales vectors before adding. Enter a coefficient for each vector. The calculator displays every scaled component.
Can I use bearings?
Yes, use azimuth or quadrant bearings. Azimuth measures clockwise from north. Quadrant bearings use north or south references.
Can results be exported?
Yes, download structured CSV output. Use print for PDF saving. The copy button includes complete calculation steps.