Vector Magnitude Calculator
Length, unit vector and direction angles in 2D or 3D.
Enter your values
Enter the x component you are working with.
Enter the y component you are working with.
Enter the z component you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Length, unit vector and direction angles in 2D or 3D. |
|---|---|
| Category | Math |
| Inputs needed | x component, y component, z component |
| Main output | Magnitude |
| Formula | |v| = √(x² + y² + z²) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- x component
- Enter the x component you are working with.
- y component
- Enter the y component you are working with.
- z component
- Enter the z component you are working with.
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.
What do I need to enter into the Vector Magnitude Calculator?
Just 3 values: x component, y component, z component. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Vector Magnitude Calculator work out the answer?
A vector's magnitude is the square root of the sum of its squared components: |v| = √(x² + y² + z²). It applies the formula |v| = √(x² + y² + z²) and shows the working so you can check each step by hand.
Is the Vector Magnitude Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.