Unit Vector Calculator

Enter the X,Y, and Z coordinates of your vector to calculate the equivalent unit vector as a ratio of the magnitude of that vector. This calculator also calculators the magnitude of the original vector, and the angle of the vector. *If only calculating the unit vector in the x and y plane, enter z as 0*

What is the unit vector?

A unit vector is the equivalent vector of your original vector that has a magnitude of 1. In other words, it has the same direction as your original vector but the total magnitude is equal to one. Since the unit vector is the originally vector divided by magnitude, this means that it can be described as the directional vector. Therefore, if you have the direction vector and the magnitude, you can calculate the actual vector.

Unit Vector Formula

The formula for the unit vector is as follows:

u = U / |U|

Where u is the unit vector, U is the original vector, and |U| is the magnitude of the original vector. To calculate the magnitude you must use the following formula.

|U| = Sqaure Root ( X^2 + Y^2+Z^2)

Keep in mind that these vectors always originate at the origin. Otherwise the formula becomes a little more complicated.

You can also use our distance calculator to determine the magnitude, since distance is another word for magnitude in coordinate systems.

Unit Vector Calculator

For more math related calculators, visit our math section.

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