📏 Vector Magnitude Calculator
Calculate vector magnitude (length)
Vector Components
How to Use This Calculator
Enter Vector Components
Input the x, y, and optionally z components of your vector. Leave z blank (or 0) for 2D vectors.
Calculate
Press "Calculate Magnitude" to find the vector's magnitude (length) using the Pythagorean theorem.
View Result
See the magnitude displayed. For 3D vectors, you'll also see the 2D magnitude (ignoring z).
Formula
2D: |v| = √(x² + y²)
3D: |v| = √(x² + y² + z²)
Example: Vector v = (3, 4)
|v| = √(3² + 4²) = √(9 + 16) = √25 = 5
Example: Vector v = (3, 4, 12)
|v| = √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13
About Vector Magnitude Calculator
The Vector Magnitude Calculator finds the magnitude (length) of a vector using the Pythagorean theorem. The magnitude represents the vector's size or length.
When to Use This Calculator
- Physics: Calculate speed, force magnitude, or distance
- Engineering: Find magnitude of forces and displacements
- Mathematics: Calculate vector lengths
- Computer Graphics: Normalize vectors and calculate distances
Frequently Asked Questions
What is vector magnitude?
Vector magnitude (|v|) is the length or size of a vector. Formula: |v| = √(x² + y² + z²). It's always non-negative and represents the distance from origin to the vector's endpoint.
Can magnitude be negative?
No! Magnitude is always non-negative (|v| ≥ 0). It represents length, which cannot be negative. Zero magnitude means zero vector (0, 0, 0).
Is magnitude the same as distance?
Yes! Vector magnitude equals the distance from the origin (0, 0, 0) to the point (x, y, z) representing the vector's endpoint.