2D Vector Addition Calculator

The 2D vector addition calculator by iCalculator is an online tool that allows you to calculate the sum of two 2D vectors with the entered values. In this modern era of technology, people want to save their time as much as possible. Why mess with a standard calculator to perform manual vector additions when you can use a good calculator specifically designed for vector addition? With these thoughts in mind, iCalculator created this free online interface( the '2D vector addition calculator' ) for you so that solving the addition of two complicated vectors gets easier for you and you get the most accurate results within seconds.

2D Vector Addition Calculator
2D Vector Addition Calculator Results

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2D Vector Addition Calculator. This image shows 2D Vector Addition with associated calculations used by the 2D Vector Addition Calculator

The advantage of the "2D Vector Addition Calculator"

Before discussing more about the calculator, let us understand some of the terms related to it.

Vector addition

Numerous operations can be performed with and upon vectors. The addition of two 2D vectors is such an operation that requires some special methods and a lot of hard work. It takes a lot of time too. That is why it is recommended to use a good calculator for performing operations that can save you time so that you can focus on other math challenges, other areas of homework or other elements of a design, engineering or challenges that you face with vectors.

When two vectors are added together, the final output is the 'resultant' of those two vectors.

For example, suppose you are applying force to an object at an angle of 30 degrees and your friend applies the same force to that object at an angle of -30 degrees, the resultant of both the forces will be zero (as the directions are opposite to each other and the forces are equal to each other). We can say that both the vectors applied in the direction of the force are added and the resultant of the force is the net force on the object. Vector addition is applied here.

Vector addition is used a lot in the field of Physics in almost each and every part and it is a very important part of our everyday life. In physics, we can add two forces (vectors) by drawing the free-body diagram of the object on which the force is applied.

There are numerous methods for calculating the addition of two vectors. Some of them are:

The Pythagorean Theorem

When two vectors make a right angle (90 degrees) to each other and if we want to find their resultant i.e., add the two vectors then Pythagorean theorem would be considered as the best method to do so. However, we can only add a maximum of two vectors at a time with the help of this method and the vectors must make an angle of 90 degrees to each other.

The mathematical formula for the Pythagoras Theorem is given by:

A2 + B2 = C2


  • A and B are the perpendicular and the base of the right-angled triangle
  • C is the hypotenuse of the triangle

Let us understand this with the help of an example. Suppose two vectors (say 'a' and 'b') are making an angle of 90 degrees to each other. If we want to sum up these two vectors, the resultant will be the vector from the tail of the vector 'a' to the tail of the vector 'b'. Let us say this resultant vector as 'c'. Then according to the Pythagorean Theorem:

c2 = a2 + b2

The Parallelogram Law

Let us suppose that two vectors (say 'a' and 'b') make an angle 'k'. We have to draw both the vectors into their appropriate direction. The other vector will be drawn from the tail of the first vector. After that, we have to complete the vectors in such a way that they make a parallelogram.

The magnitude and direction of the resultant vector (i.e., the resulting vector after the sum of both the vectors) will be given by the diagonal of the parallelogram.

Trigonometric calculation

When two coplanar vectors are forming a non-right angled triangle, we can find the sum of those vectors i.e., the resultant vector with the help of "the sine rule" and the "cosine rule".

The formula for the cosine rule is given by:

FR = [F12 + F22 - 2F1F2 cos(1800 - x)]½


  • F1 is the first coplanar vector
  • F2 is the second coplanar vector
  • FR is the resultant vector of the two coplanar vectors
  • 'x' is the angle between the two coplanar vectors

The Triangle Rule

Let us suppose that two vectors are drawn at an angle 'x' with each other. The head of one vector coincides with the tail of the other vector. The vectors formed after joining the tail and the head of the first and second vector respectively is known to be the resultant of those two vectors.


If you have read this far thank you, we hope that although vector math can be complicated and difficult to solve as in the addition of two 2D vectors we covered above, if you want to simplify your calculation, you will have the confidence to use this good calculator, online, anytime and enjoy its reliability.

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