How to use the vector magnitude and direction calculator
Find the length and direction angle of a two-dimensional vector. Enter x-component, y-component in the fields above; the magnitude, direction angle are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “vector magnitude”, “direction angle of vector”, “polar form of vector”, “calculate vector magnitude and direction”, “find magnitude”.
Formula
Variables
- vx — x-component
- vy — y-component
Worked example
With x-component = 3, y-component = 4, the calculator gives magnitude ≈ 5; direction angle ≈ 53.1301 °.
Frequently asked questions
What is the vector magnitude and direction calculator used for?
Find the length and direction angle of a two-dimensional vector. It helps with questions such as “vector magnitude”, “direction angle of vector”, “polar form of vector”.
What is the formula for the vector magnitude and direction calculation?
Magnitude = √(vx × vx+vy × vy). Direction angle (°) = atan2d(vy,vx). Here vx is x-component, vy is y-component.
What inputs do I need for the vector magnitude and direction calculator?
You need x-component, y-component. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the vector magnitude and direction calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the vector magnitude and direction result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.