Vectors describe quantities with both size and direction, such as velocity and force.
How to use the Vector Magnitude and Angle Calculator
- x component
- y component
- z component
Results update as you type, and every field accepts the units shown in its menu.
How it works
Square each component, add them and take the square root. The unit vector divides each component by the magnitude.
Inputs explained
| Field | What to enter |
|---|---|
| x component | A number |
| y component | A number |
| z component | A number |
What each result means
- Magnitude = sqrt([x component]^2 + [y component]^2 + [z component]^2)
- Unit vector x = [x component]÷[Magnitude]
- Unit vector y = [y component]÷[Magnitude]
- Unit vector z = [z component]÷[Magnitude]
- Angle with x-axis = deg(acos([x component]÷[Magnitude]))
Example values
How the main result changes when x component changes and everything else stays at the example values above:
| x component | Magnitude |
|---|---|
| 1.5 | 12.7377 |
| 2.25 | 12.8477 |
| 3 | 13 |
| 3.75 | 13.1933 |
| 4.5 | 13.4257 |
| 6 | 14 |
Formula
|v| = √(x² + y² + z²)Worked example
Inputs — x component: 3; y component: 4; z component: 12.
Results — Magnitude = 13; Unit vector x = 0.230769; Unit vector y = 0.307692; Unit vector z = 0.923077; Angle with x-axis = 76.6576 °.
Frequently asked questions
How do I use it for a 2D vector?
Set z to 0.
What is a unit vector?
A vector of length 1 pointing in the same direction.
What formula does the Vector Magnitude and Angle Calculator use?
|v| = √(x² + y² + z²).