Math

Instant, private, and free

Vector Direction Calculator.

Calculate direction angles and magnitude for a three-dimensional vector.

On-device calculationNo signup
01

Set your values

Results update as you type.

Direction angle x: 76.657636

Direction angle x

0.000000
Direction angle y: 72.079787

Direction angle y

0.000000
Direction angle z: 22.619865

Direction angle z

0.000000
Magnitude: 13

Magnitude

0.000000

Results update automatically as you type.

Use Cases

Physics and Engineering

Determine the orientation of a force, velocity, or acceleration vector in 3D space, which is essential for analyzing motion and forces.

Example: Find the direction angles of a force vector with components (3, 4, 5) N.

3D Graphics and Game Development

Calculate the direction of a 3D model's orientation or the direction of a light source to set up scenes and animations.

Example: Set the direction of a spotlight with direction vector (1, -1, 2).

Frequently Asked Questions

How does the Vector Direction Calculator determine direction?
The calculator uses the standard mathematical formula for vector direction in 3D space. Given the x, y, and z components, it computes the direction angles (alpha, beta, gamma) relative to the x, y, and z axes using the arccosine of the component divided by the vector's magnitude.
What do the direction angles represent?
The direction angles are the angles between the vector and each positive coordinate axis. For a vector with components (x, y, z), the angle with the x-axis is arccos(x/|v|), with the y-axis is arccos(y/|v|), and with the z-axis is arccos(z/|v|), where |v| is the magnitude.
Can I use this calculator for 2D vectors?
Yes, you can enter the x and y components and leave the z component as 0. The calculator will then compute the direction angles in the xy-plane, with the z-angle being 90 degrees.

Tips & Common Mistakes

Tips

  • Ensure all components are entered as numbers; you can use decimals or integers.
  • If you have a 2D vector, simply enter 0 for the z component.
  • The direction angles are in degrees; you can convert to radians if needed for further calculations.
  • Double-check the sign of your components, as negative values will produce angles greater than 90 degrees.

Common Mistakes to Avoid

  • Forgetting to include the z component when working in 3D, which leads to incorrect direction angles.
  • Entering the magnitude instead of the components; the calculator expects the x, y, and z values.
  • Misinterpreting the direction angles as the angles between the vector and the xy-plane, when they are actually with each axis.

Last updated: August 13, 2026