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 calculates the magnitude of the original vector, and the angle of the vector.

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

How to calculate a unit vector

We will now take a look at en example of how you can calculate a unit vector from a normal vector. Let’s take a vector u = (5,-4,2).

  1. First, you must calculate the magnitude of the vector. This is done through the following formula. |u| = √(x₁² + y₁² + z₁²)
  2. Plug in the values into the formula above, and you should get 6.708.
  3. Next, you need to divide each unit vector point by the magnitude. This is because the unit vector has a magnitude of 1. Dividing the original vector by it’s magnitude achieves that rule.
  4. This should yield X = .706, Y= – .596, Z = .298
  5. Check the result with the calculator above.

Now you know how to calculate a unit vector, but what happens if the vector is given as two points and neither are position at the origin? If this is the case, the steps for solving the unit vector are a little different. Let’s take a vector with points (7,8,9) and (2,5,1)

  1. First, you must understand that a vector, as mentioned earlier, describes a direction and magnitude. Since both these values are independent of position, you can manipulate a vector to re-position it at the origin
  2. Now that you know this, you can place the vector at the origin simply by subtracting one vector from the other. In this case (7,8,9) – (2,5,1) = (5,3,8). You just subtract each coordinate point from the other.
  3. Now that you have the vector placed at the origin, complete steps 1-5 from above and you have your unit vector!

For more math related calculators, visit our math section.

Related Terms

unit vector calculator
unit vector formula
how to calculate unit vector
how to find unit vector
find unit vector
unit tangent vector calculator
unit normal vector calculator
unit vector equation
find a unit vector in the direction of the given vector
orthogonal unit vectors
binormal vector calculator
unit vector perpendicular to two vectors
find two unit vectors orthogonal to
unit normal vector formula
unit vector of a vector
how to find direction vector
find a unit vector that is orthogonal to both
find the unit vector in the direction of
how to find unit tangent vector
find a unit vector in the direction of the given vector calculator
find the unit vector in the same direction as v
how to find unit normal vector
unit vector perpendicular to a and b
unit vector formula 3d
how to get unit vector
unit vector perpendicular to a vector
principal unit normal vector calculator
find unit vector calculator
unit vector perpendicular to plane
how to find a unit vector perpendicular to two vectors
direction vector formula
find the unit tangent vector
how to find unit vector from two points
find two unit vectors orthogonal to both
how to find a unit vector in the same direction
find a vector that has the same direction as
find a unit vector that is orthogonal to both u and v
find a unit vector perpendicular to
find a unit vector perpendicular to the plane of triangle abc
unit vector perpendicular to a plane
find a unit vector perpendicular to both the vectors
direction vector calculator
unit tangent calculator
find a unit vector perpendicular to each of the vectors
find unit vector perpendicular to plane
find the unit vector that has the same direction as the vector v
find a unit vector in the direction of the vector
find unit vector perpendicular to a and b
find a unit vector perpendicular to both a and b
how to find the unit vector of a vector
find the unit vector having the same direction as v
how to find unit vector perpendicular to a vector
how to find unit vector of a vector
find the unit vector perpendicular to each of the vectors
find unit vector perpendicular to vector
find a unit normal vector to the surface at the given point
find unit normal vector
how do you find the unit vector
find a unit vector in xy plane which makes an angle of 45
how to find a unit vector perpendicular to a vector
find a unit vector in the same direction as
unit normal calculator
unit vector with same direction
find the unit vector perpendicular to both the vectors a and b
how to find a vector in the opposite direction
find the unit vector perpendicular to
unit normal vector equation
find the unit tangent vector of the given curve
find a unit vector perpendicular to the plane abc
how to find the unit normal vector
how to calculate the unit vector
find two unit vectors orthogonal to one vector
find unit vector perpendicular to two vectors
unit vector in same direction
unit vector calculator 3d
unit vector of two vectors
finding unit tangent vector
find the unit vector calculator
find unit vector orthogonal to two vectors
unit vector formula 2d
formula to find unit vector
find a vector that has the same direction as but has length 6
how to find unit vector 3d
unit vector in the direction of a vector
how to determine unit vector
unit vector same direction
unit vector perpendicular to both a and b
how do you find a unit vector
find the unit vector perpendicular to both the vectors
find a unit vector perpendicular to both
find direction vector
how to get the unit vector
how to find a unit vector in the direction of the given vector
find a unit vector in the direction of the resultant of the vectors
find a unit vector normal to the surface
find the unit vector perpendicular to the plane
how to find unit vector perpendicular
formula for unit tangent vector
unit vector in direction of given vector
magnitude of unit vector formula
finding a unit vector in the same direction
formula for unit normal vector
principal unit normal vector formula
find a unit vector for which the directional derivative is zero
determine a unit vector perpendicular to both
determine unit vector
find two unit vectors that are normal to the plane determined by the points
how to find unit vector perpendicular to plane
find unit vector perpendicular
find unit vector in the direction of
unit vector notation formula
find a vector in the direction of another vector
determine a unit vector which is perpendicular to both
find two unit vectors that are orthogonal to both
find a unit vector normal to the plane
vector unit formula
find unit vector in opposite direction
find the unit vector with the same direction as
find two unit vectors orthogonal calculator
unit vector how to find
find unit vector in direction of
how to find unit vector of two vectors
how to find unit normal vector to a surface
find the unit vector perpendicular to both a and b
how to find the unit vector perpendicular to two vectors
unit vector orthogonal to a vector
find a vector of length 3 with the same direction as
determine the unit vector perpendicular to the plane
find a unit vector in the opposite direction of v
find a unit vector in the same direction
find the unit vector that is perpendicular to both a and b
unit vector perpendicular to vector
find direction vector from two points
how to find unit normal vector of a surface
how to find unit vector in the direction of the given vector
find the unit normal vector to the surface at the point
find the unit vector in the direction
how to determine a unit vector
how to find magnitude of unit vector
find unit vector in the direction of the given vector
find the magnitude and direction angle for each vector
find the unit vector with direction angles
find unit vector normal to plane
how to find unit vectors in spherical coordinates
the unit vector of a vector a of magnitude 2 is
find the unit normal to the surface
solve for x each figure is a parallelogram calculator
determine the unit vector perpendicular to both
how to find unit vector in direction of given vector
unit tangent and normal vector calculator
find vector in opposite direction
calculate unit tangent vector
find a unit vector which is perpendicular to both
how to find the unit normal vector of a surface
how to find unit vector perpendicular to a plane
find the unit vector normal to the surface
the unit vector in the same direction as
equation of unit vector
find unit vector normal to the surface
find the two unit vectors orthogonal to both
formula for finding unit vector
how to find direction of unit vector
unit normal formula
formula for unit vector perpendicular
how to find unit vector with same direction
find a unit vector perpendicular to plane pqr
find a unit vector that has the same direction as the vector
unit normal vector to a surface formula
how to find the unit vector in the direction of v
find unit vector in direction of vector
how to find unit normal to a surface
how to find a unit vector of a vector
how to find the unit vector of two vectors
unit vector solver