Vector analysis
Calculation steps
Calculator settings
Interactive vector graph
Inspect components, angles, origins, endpoints, and resultants.
Calculation history
Formula used
How to use this calculator
Select a mode and enter the required vector values. Choose angle units, direction, range, and precision before calculating. Results appear above the form with detailed calculation steps.
Use the graph controls to inspect vector direction and components. Export the result as CSV, PDF, copied text, or an image. Saved calculations remain available in your browser history.
Example data
| Mode | Input | Expected result |
|---|---|---|
| Cartesian to polar | x = 3, y = 4 | r = 5, θ ≈ 53.130102° |
| Polar to Cartesian | r = 10, θ = 30° | x ≈ 8.660254, y = 5 |
| Two points | (1, 2) to (6, 8) | v = ⟨5, 6⟩, r ≈ 7.81025 |
| Dot product | A = ⟨3,4⟩, B = ⟨−2,5⟩ | A · B = 14 |
Frequently asked questions
What is a polar vector?
A polar vector uses magnitude and direction. It represents the same vector as Cartesian components.
Why does this calculator use atan2?
The atan2 function preserves quadrant information. It also handles vertical vectors more reliably.
Can the angle be negative?
Yes. Choose the signed range option. Negative angles follow your selected rotation direction.
What happens with a zero vector?
Its magnitude is zero. Its direction and unit vector remain undefined.
Can I use radians or gradians?
Yes. Select your preferred angle unit. All displayed angles follow that setting.
How are compass bearings handled?
Compass bearings begin at north. They increase clockwise under standard bearing conventions.
Does a negative magnitude work?
Yes. The calculator converts it to positive magnitude. It also rotates direction by half a turn.
Can I calculate several vectors together?
Yes. Use batch mode for multiple lines. The calculator also reports their resultant vector.
Are my history entries uploaded?
No. History stays inside local browser storage. Clearing browser data can remove it.