Vector Magnitude Calculator
Length, unit vector and direction angles in 2D or 3D.
Enter your values
ⓘ Live results
Results
- Magnitude
- 13
- Unit vector
- (0.2308, 0.3077, 0.9231)
- Angle from x-axis
- 76.66°
- Angle from y-axis
- 72.08°
- Angle from z-axis
- 22.62°
- 2D angle in the xy-plane
- 53.13°
Quick answer
A vector's magnitude is the square root of the sum of its squared components: |v| = √(x² + y² + z²).
|v| = √(x² + y² + z²)
How to use the Vector Magnitude Calculator
- 1Enter the x and y components.
- 2Leave z as 0 for a 2D vector.
- 3Use the unit vector when you need direction without magnitude.
Worked example
Using the values the calculator loads with:
Inputs
- x component3
- y component4
- z component12
Results
- Magnitude13
- Unit vector(0.2308, 0.3077, 0.9231)
- Angle from x-axis76.66°
- Angle from y-axis72.08°
- Angle from z-axis22.62°
- 2D angle in the xy-plane53.13°
Frequently asked questions
What is a unit vector for?
It carries pure direction — multiply it by any length to build a vector pointing the same way.
Are direction cosines the same thing?
Yes, the unit vector's components are the cosines of the angles with each axis, and their squares sum to 1.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.