Find the magnitude, unit vector, and direction angles for a 2D or 3D vector.
Last updated: June 2026 | By Patchworkr Team
Enter all three vector components as real numbers.
Direction describes where the vector points, independent of its length.
The zero vector has no direction, so the calculator rejects it.
1. Choose 2D or 3D.
2. Enter the vector components.
3. Read the live magnitude, unit vector, and direction angles.
For the 3D vector (3, 4, 12):
magnitude = sqrt(3^2 + 4^2 + 12^2) = 13
unit vector = (3/13, 4/13, 12/13)
The direction is undefined, so the tool shows an error.
Yes. Negative values mean the vector points toward the negative axis direction.
Yes. 2D direction can be expressed by a single angle from the positive x-axis.
Yes, subject only to floating-point rounding in the display.
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