Can this calculator be used for 2D vectors?

Yes. For 2D vector addition or subtraction, simply enter 0 for the z-components.

Vector Addition Calculator

Q: How do you add two vectors?

To add two vectors, add their corresponding x, y, and z components: A + B = (Ax + Bx, Ay + By, Az + Bz).

Q: How do you subtract two vectors?

To subtract two vectors, subtract the components of the second vector from the first: A - B = (Ax - Bx, Ay - By, Az - Bz).

Q: What is a vector sum?

The vector sum is the resultant vector obtained by adding two or more vectors component by component.

Use this vector addition calculator to add vectors and subtract vectors in 2D or 3D. It works as an adding vectors calculator, add vectors calculator, vector sum calculator, and vector subtraction calculator.

Add and Subtract Two Vectors

Enter the x, y, and z components of vectors A and B. The results update automatically.

Vector Inputs

Vector A x-component [Ax]

Vector A y-component [Ay]

Vector A z-component [Az]

Vector B x-component [Bx]

Vector B y-component [By]

Vector B z-component [Bz]

Use “.” as the decimal separator.

Results

A + B = (Ax + Bx, Ay + By, Az + Bz)
A − B = (Ax − Bx, Ay − By, Az − Bz)

Vector	x	y	z
A + B	—	—	—
A − B	—	—	—

Meaning of the result

Enter two vectors to calculate their vector sum and vector subtraction instantly.

Vector Addition Diagram

The diagram shows vector addition using the head-to-tail method. Vector B starts at the tip of vector A, and the resultant A + B runs from the origin to the final tip. For 2D vectors, set both z-components to 0.

Vector Addition and Subtraction Formulas

A + B = (Ax + Bx, Ay + By, Az + Bz)

A − B = (Ax − Bx, Ay − By, Az − Bz)

Ax, Ay, Az = components of vector A
Bx, By, Bz = components of vector B
A + B = vector sum
A − B = vector subtraction result

This calculator adds and subtracts vectors component by component for both 2D and 3D cases.

How to Use the Vector Addition Calculator

Enter the x, y, and z components of vector A.
Enter the x, y, and z components of vector B.
The calculator automatically finds A + B and A − B.
For 2D vectors, enter 0 for both z-components.
You can also use the Calculate button for a manual refresh.

Examples

Example 1: 3D vector addition

Let A = (5, -6, 3) and B = (-7, 0, 10).

A + B = (5 - 7, -6 + 0, 3 + 10) = (-2, -6, 13)

A − B = (5 - (-7), -6 - 0, 3 - 10) = (12, -6, -7)

Example 2: 2D vector addition

Let A = (4, 1, 0) and B = (2, -3, 0).

A + B = (6, -2, 0)

A − B = (2, 4, 0)

What This Calculator Helps You Find

This page is useful for searches such as vector addition calculator, adding vectors calculator, add vectors calculator, addition of vectors calculator, vector sum calculator, vector summation calculator, vector subtraction calculator, and sum of vectors calculator.

FAQ

How do you add two vectors?

Add the corresponding x, y, and z components of the two vectors.

How do you subtract two vectors?

Subtract the corresponding components of vector B from vector A.

Can this page calculate 2D vectors?

Yes. For 2D vectors, just use 0 for the z-components.

What is a vector sum?

A vector sum is the resultant vector obtained by adding vectors component by component.

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References

Giancoli, Douglas C. Physics: Principles with Applications. Pearson.
Standard introductory physics treatment of vectors and component methods.