Vector Magnitude Calculator
Magnitude of 2-D or 3-D vectors, with exact fractions and the working.
Change the values and press Calculate to work out your own figures.
Enter the vector components (leave z blank for 2-D).
Show the working
- |a| = √(3² + 4²) = √25
How to use it
Enter the vector components (leave z blank for 2-D).
Enter coordinates as whole numbers, decimals or fractions (3/4). Show the working gives the formula with your numbers.
Key facts
|a| = √(a_x² + a_y² + a_z²)
Components
Enter the x-, y- and (optionally) z-components; leave z blank for vectors in a plane.
Questions
How is the magnitude worked out?
|a| = √(a_x² + a_y² + a_z²)
Can I use fractions?
Yes, such as 1/2 or -3/4.
Formulas
|a| = √(a_x² + a_y² + a_z²)
Sources
Limitations
- Vectors have two or three components (leave z blank for 2-D).
- Earth distances assume the WGS 84 ellipsoid (sea level).