Determine the coordinates of the end point of the vector. For example, an object having three forces pushing against it--one pushing 3 units right, one pushing 4 units up and one pushing 12 units back--would have the coordinates (3, 4, 12).
Calculate the square root of x^2 plus y^2, where x is the x-coordinate and y is the y-coordinate. In this example, x would be 3 and y would be 4, so the number would be 5.
Use the number just calculated as "a" and the z-coordinate for "z" and calculate the square root of a^2 + z^2. This number will be the magnitude of the vector. For example, 5 squared plus 12 squared is 169. The square root of 169 is 13. Therefore, the vector's magnitude is 13.