How Do You Calculate Magnitude and Direction?

Vectors are important tools used to illustrate movement and elements, such as force in physics. In order to work with vectors, you have to understand how to find their direction and magnitude. In many cases, materials like grid paper, a protractor, a ruler, and a calculator are necessary.

  1. Figure out your units

    Vectors are represented by arrows of a particular length pointing in a particular direction. Even if you know the formulas, you won't be able to measure magnitude or direction unless you know the units. The magnitude of the vector is the length, but the length might represent miles per hour, meters per second, and so on. For direction, vectors are often expressed in terms of degrees from 0, although sometimes they are given based on cardinal directions or the slope of the line created on an x-y plot.

  2. Calculate the magnitude

    Sometimes you can measure the magnitude with a ruler and convert the units by calculator if you know that, for example, 1 inch equals 10 meters per second. You will often be given points on a grid, and you will have to calculate the magnitude using the Pythagorean theorem. This states that the summed squares of the base and height of a right triangle equal the square of the hypotenuse (a^2+b^2=c^2).

  3. Calculate the direction

    The direction can often be measured with a protractor. Place the bottom of the protractor along the line that represents 0 degrees and determine at what angle the vector is. Convert your angle so it is relative to the nearest cardinal direction if necessary.