# Vector Addition Calculator

This online calculator performs vector addition and displays vectors and vector sum graphically.

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Below you can find vector addition calculator. It calculates the vector sum every time you add an entry into vectors table and also displays results graphically. I've tried to make it as universal as possible, thus you can add vector using two alternative notations - cartesian coordinates (see Cartesian coordinate system) and polar coordinates (see Polar coordinate system). If you choose cartesian, you need to enter x and y components (or coordinates) of a vector. If you choose polar, you need to enter radial (often called the magnitude) and angular (often called the polar angle) components (or coordinates) of a vector. Note that angular coordinate can be entered either as degrees or as radians. Additional details regarding how an addition is performed and how to perform a subtraction can be found below the calculator

#### Vectors

arrow_upwardarrow_downwardCoordinate system | arrow_upwardarrow_downwardX coordinate | arrow_upwardarrow_downwardY coordinate | arrow_upwardarrow_downwardRadial coordinate | arrow_upwardarrow_downwardAngular coordinate | arrow_upwardarrow_downwardUnits | ||
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#### Vector sum

Internally, calculator converts all entered vectors into cartesian form. It calculates their x and y coordinates using the following conversion formulas:

Then it performs the vector addition, which is very simple and where the vector sum can be expressed as follows:

For vectors and the vector sum is

All entered vectors and their sum are also plotted on graph below the results, so you can see the graphical result of the operation, where the vector sum is shown in red. The vector sum is plotted by placing vectors head to tail and drawing the vector from the free tail to the free head (so-called **Parallelogram law**).

And of course you can use this calculator to calculate vector difference as well, that is, the result of subtracting one vector from another. This is due to the fact, that the vector difference is a vector sum with the second vector reversed, according to:

To get reversed, or opposite vector in cartesian form, you simply negate the coordinates. In polar form you can either add 180 degrees to angular coordinate, or negate the radial coordinate (either method should work).

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